# gst: evolving fractal dimensions in iterative bicolored percolation.

<< ️Criticality is traditionally regarded as an unstable, fine-tuned fixed point of the renormalization group. (AA)  introduce an iterative bicolored percolation process in two dimensions and show that it can both preserve criticality and transform fractal dimensions. >>

<< ️Starting from critical configurations, such as the O⁡(𝑛) loop and fuzzy Potts models, successive coarse graining generates a hierarchy of distinct yet critical generations. Using the conformal loop ensemble, (They) derive exact, generation-dependent fractal dimensions, which are quantitatively confirmed by large-scale Monte Carlo simulations. The evolutionary trajectory depends not only on the universality class of the initial state but also on whether it possesses a two-state critical structure, leading to different critical exponents starting from site and bond percolation. >>

<< ️These results establish a general geometric mechanism for evolving fractal dimensions, in which scale invariance persists across generations. >>

Shuo Wei, Haoyu Liu, Xin Sun, et al. Evolving fractal dimensions in iterative bicolored percolation. Phys. Rev. E 113, L032102. Mar 23, 2026.

https://journals.aps.org/pre/abstract/10.1103/s2ql-zxz6#4eafda38-c97e-4656-8034-9a3682fa0218

arXiv: 2511.18462v2 [cond-mat.stat-mech]. Mar 24, 2026. 

https://arxiv.org/abs/2511.18462

Also: order, disorder, fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, order, disorder, fluctuations, percolation, fractal dimensions, criticality, coarse-graining transformations.

# gst: apropos of ab.normal criticalities, a hypothetical scenario of non-normal route to chaos.

<< ️Deterministic chaos is commonly associated with spectral criticality: exponential sensitivity is expected when Jacobian eigenvalues exceed unity in parts of the attractor, producing the local expansion that offsets contraction elsewhere. (AA) show that this paradigm is incomplete in dimensions d>1.  >>

<< ️(They) construct a bounded 3D dynamical system whose Jacobian is pointwise spectrally contracting, namely all instantaneous eigenvalues remain strictly inside the stability region, yet the system develops a positive maximal Lyapunov exponent and undergoes a transition to chaos as a non-normality index increases at fixed spectral radius. The mechanism relies on the repeated regeneration of transient non-normal amplification through endogenous switching that reinjects trajectories into amplifying non-orthogonal directions. >>

<< ️Although demonstrated here for a discrete-time map, the mechanism is geometric and applies more broadly to deterministic dynamical systems. These results show that chaos can emerge without spectral criticality and identify non-normality as an independent route to deterministic chaos. >>

D. Sornette, V.R. Saiprasad, V. Troude. Non-Normal Route to Chaos. arXiv: 2603.08191v1 [nlin.CD]. Mar 9, 2026.

https://arxiv.org/abs/2603.08191

Also:  Virgile Troude, Sandro Claudio Lera, Ke Wu, Didier Sornette. Illusions of Criticality: Crises Without Tipping Points. arXiv: 2412.01833v5 [nlin.CD]. Oct 3, 2025. https://arxiv.org/abs/2412.01833

Also: chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, criticality, transitions, non-normality, transient non-normality, reinjection via endogenous switch.

# gst: predicting oscillations in complex networks with delayed feedback.

<< ️Oscillatory dynamics are common features of complex networks, often playing essential roles in regulating function. Across scales from gene regulatory networks to ecosystems, delayed feedback mechanisms are key drivers of system-scale oscillations. >> 

<< ️The analysis and prediction of such dynamics are highly challenging, however, due to the combination of high-dimensionality, non-linearity and delay. Here, (AA) systematically investigate how structural complexity and delayed feedback jointly induce oscillatory dynamics in complex systems, and introduce an analytic framework comprising theoretical dimension reduction and data-driven prediction. >>

<< ️(They) reveal that oscillations emerge from the interplay of structural complexity and delay, with reduced models uncovering their critical thresholds and showing that greater connectivity lowers the delay required for their onset. (Their) theory is empirically tested in an experiment on a programmable electronic circuit, where oscillations are observed once structural complexity and feedback delay exceeded the critical thresholds predicted by our theory. >>

<< ️Finally, (They) deploy a reservoir computing pipeline to accurately predict the onset of oscillations directly from timeseries data. (AA) findings deepen understanding of oscillatory regulation and offer new avenues for predicting dynamics in complex networks. >>

Shijie Liu, Jinliang Han, Jianming Liu, et al. Predicting oscillations in complex networks with delayed feedback. arXiv: 2603.04251v2 [cond-mat.dis-nn]. Mar 4, 2026.

https://arxiv.org/abs/2603.04251

Also: network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, oscillatory dynamics, oscillatory regulations, system-scale oscillations, delay, delayed feedback mechanisms, criticality, critical thresholds.

# gst: localization of information driven by stochastic resetting.

<< ️The dynamics of extended many-body systems are generically chaotic. Classically, a hallmark of chaos is the exponential sensitivity to initial conditions captured by positive Lyapunov exponents. Supplementing chaotic dynamics with stochastic resetting drives a sharp dynamical phase transition: (AA) show that the Lyapunov spectrum, i.e., the complete set of Lyapunov exponents, abruptly collapses to zero above a critical resetting rate. >>

<< ️At criticality, (They) find a sudden loss of analyticity of the velocity-dependent Lyapunov exponent, which (They) relate to the transition from ballistic scrambling of information to an arrested regime where information becomes exponentially localized over a characteristic length diverging at criticality with an exponent 𝜈=1/2 and a dynamical exponent 𝑧=2. (They) illustrate (Their) analytical results on generic chaotic dynamics by numerical simulations of coupled map lattices. >>

Camille Aron, Manas Kulkarni. Localization of information driven by stochastic resetting. Phys. Rev. E 113, L022101. Feb 23, 2026.

https://journals.aps.org/pre/abstract/10.1103/pkgb-mp8s

arXiv:2510.07394v2 [cond-mat.stat-mech]. Feb 24, 2026.

https://arxiv.org/abs/2510.07394

Also: chaos, random, transition, collapse, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, transition, collapse, randomness, stochasticity, stochastic resetting, phase transition, criticality, critical resetting rate, ballistic scrambling of information.

# gst: fractals in rate-induced tipping.

<< ️When parameters of a dynamical system change sufficiently fast, critical transitions can take place even in the absence of bifurcations. This phenomenon is known as rate-induced tipping and has been reported in a variety of systems, from simple ordinary differential equations and maps to mathematical models in climate sciences and ecology. In most examples, the transition happens at a critical rate of parameter change, a rate-induced tipping point, and is associated with a simple unstable orbit (edge state). >>

<< ️In this work, (AA) show how this simple picture changes when non-attracting fractal sets exist in the autonomous system, a ubiquitous situation in non-linear dynamics. (They) show that these fractals in phase space induce fractals in parameter space, which control the rates and parameter changes that result in tipping. (They) explain how such rate-induced fractals appear and how the fractal dimensions of the different sets are related to each other. >>

<< ️(AA) illustrate (Their) general theory in three paradigmatic systems: a piecewise linear one-dimensional map, the two-dimensional Hénon map, and a forced pendulum. >>

Jason Qianchuan Wang, Yi Zheng, Eduardo G. Altmann. Fractals in rate-induced tipping. arXiv: 2601.16373v1 [nlin.CD]. Jan 23, 2026.

https://arxiv.org/abs/2601.16373

Also: transition, pendulum, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transitions, pendulum, forced pendulum, fractals, absence of bifurcations, rate-induced tipping, criticality.

# gst: directionality and node heterogeneity reshape criticality in hypergraph percolation.

<< Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of others only weakens interactions. Metabolic reaction networks offer an intuitive example of such asymmetric dependencies. >>

<< Here (AA) develop a message-passing and statistical mechanics framework for percolation in directed hypergraphs that explicitly incorporates directionality and node heterogeneity. Remarkably, (They)  show that these hypergraph features have a fundamental effect on the critical properties of hypergraph percolation, reshaping criticality in a way that depends on network structure. >>

<< Specifically, (AA) derive anomalous critical exponents that depend on whether node or hyperedge percolation is considered in maximally correlated, heavy-tailed regimes. These theoretical predictions are validated on synthetic hypergraph models and on a real directed metabolic network, opening new perspectives for the characterization of the robustness and resilience of real-world directed, heterogeneous higher-order networks. >>

Yunxue Sun, Xueming Liu, Ginestra Bianconi. Directionality and node heterogeneity reshape criticality in hypergraph percolation. arXiv: 2601.20726v1 [cond-mat.dis-nn]. Jan 28, 2026.

https://arxiv.org/abs/2601.20726

Also: network, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, transitions, criticality, hypergraph, percolation, anchor nodes.

# gst: from chimera states to spike avalanches and quasicriticality; the role of superdiffusive coupling.

<< ️The partial synchronization states of collective activity, as well as the spike avalanches realization in systems of interacting neurons, are extremely important distinguishing features of the neocortical circuits that have multiple empirical validations. However, at this stage, there is a limited number of studies highlighting their potential interrelationship at the level of nonlinear mathematical models. >>

<< ️In this study, (AA) investigate the development of chimera states and the emergence of spike avalanches in superdiffusive neural networks, as well as analyze the system's approach to quasicriticality. >>

<< ️The analysis of the available ideas suggests that partial synchronization states, spike avalanches, and quasicritical neuronal dynamics are all directly implicated in core cognitive functions such as information processing, attention, and memory. Given this fundamental role, the results presented in this (AA) work could have significant implications for both theoretical neuroscience and applied machine learning, particularly in the development of reservoir computing systems. >>

I. Fateev, A. Polezhaev. From chimera states to spike avalanches and quasicriticality: The role of superdiffusive coupling. Phys. Rev. E 113, 014215. Jan 20, 2026.

https://journals.aps.org/pre/abstract/10.1103/rmx5-8fys

Also: network, brain, neuro, behav, chimera, random, walk, walking, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, neuronal network models, chimera, random, walk, walking, avalanches, neuronal avalanches, collective behaviors, criticality.

# gst: quantum avalanche stability of many-body localization with power-law interactions.

<< ️(AA) investigate the stability of the many-body localized (MBL) phase against quantum avalanche instabilities in a one-dimensional Heisenberg spin chain with long-range power-law interactions (V ∝ r−α). >>

<< ️(They) finite-size scaling analysis of entanglement entropy identifies a critical interaction exponent αc ≈ 2, which separates a fragile regime, characterized by an exponentially diverging critical disorder, from a robust short-range regime. >>

<< ️(AA) results confirm that the MBL phase remains asymptotically stable in the thermodynamic limit when disorder exceeds an interaction-dependent threshold. >>

Longhui Shen, Bin Guo, Zhaoyu Sun. Quantum Avalanche Stability of Many-Body Localization with Power-Law Interactions. arXiv: 2601.13485v1 [cond-mat.dis-nn]. Jan 20, 2026.

https://arxiv.org/abs/2601.13485

Also: disorder, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, avalanche, avalanche stability, entanglement entropy, criticality. 

# brain: abrupt over gradual learning in the differential reinforcement of response duration task.

<< ️Learning can occur in markedly different ways: in some cases, it unfolds as a gradual process, with behavior improving slowly toward an asymptotic level of performance; in others, it appears as an abrupt process that sharply separates behavior before and after a change point. Under-standing the behavioral and neural processes underlying these distinct acquisition patterns may be critical for elucidating the basic principles of learning. >>

<< ️(AA) investigated this question experimentally using naïve rats performing a differential reinforcement of response duration (DRRD) task, in which animals were required to remain inside a nosepoke for a minimum duration of 1.5 seconds to get a sugar pellet as a reward. All rats learned to wait longer in the nosepoke when comparing behavior at the beginning and at the end of the experiment. (They) tested several continuous models against a single change point (CP) model, in which behavior changes at a specific moment and remains stable thereafter. Instead of the traditional approach based on trial-segmented behavior, (AA) used the real time elapsed since the beginning of the experiment as a continuous, uncontrolled variable. (They) fitted all models to data from individual rats and compared model fit quality across alternatives. >>

<< ️(AA) results provide strong evidence in favor of an abrupt change, as captured by the CP model, over all other models. Moreover, the residuals of the CP model exhibited a Gaussian distribution, suggesting that no additional systematic dynamics remained unexplained and that the behavioral dynamics were fully captured by a single change point. >>

Mateus Gonzalez de Freitas Pinto, Alexei Magalhães Veneziani, Marcelo Bussotti Reyes. Evidence in favor of abrupt over gradual learning in the differential reinforcement of response duration (DRRD) task. bioRxiv. doi: 10.64898/ 2025.12.26.696617. Dec 27, 2025.

https://www.biorxiv.org/content/10.64898/2025.12.26.696617v1

Also: brain, behav, in https://www.inkgmr.net/kwrds.html 

Keywords: brain, behavior, cognition, learning, change point models, criticality.

# gst: compressed self-avoiding walks in two and three dimensions.

<< ️(AA) consider the phase transition induced by compressing a self-avoiding walk in a slab where the walk is attached to both walls of the slab in two and three dimensions, and the resulting phase once the polymer is compressed. The process of moving between a stretched situation where the walls pull apart to a compressed scenario is a phase transition with some similarities to that induced by pulling and pushing the end of the polymer. >>

<< ️However, there are key differences in that the compressed state is expected to behave like a lower dimensional system, which is not the case when the force pushes only on the end point of the polymer. (They) use scaling arguments to predict the exponents both associated with the phase transition and in the compressed state and find good agreement with Monte Carlo simulations. >>

C. J. Bradly, N. R. Beaton, A. L. Owczarek. Compressed self-avoiding walks in two and three dimensions. Phys. Rev. E 112, 054126. Nov 17, 2025.

https://journals.aps.org/pre/abstract/10.1103/wtrv-4g4h

arXiv: 2506.11433v2 [cond-mat.stat-mech]. Oct 23, 2025.

https://arxiv.org/abs/2506.11433

Also: transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transitions, phase transitions, self-avoiding walk, criticality, polymer conformation, topology.

# brain: meditative absorption shifts brain dynamics toward criticality.

<< ️Criticality describes a regime between order and chaos that supports flexible yet stable information processing. Here (AA) examine whether neural dynamics can be volitionally shifted toward criticality through the self-regulation of attention. >>

<< (They) examined ten experienced practitioners of meditation during a 10-day retreat, comparing refined states of meditative absorption, called the jhanas, to regular mindfulness of breathing. (They) collected electroencephalography (EEG) and physiological data during these practices and quantified the signal's dynamical properties using Lempel-Ziv complexity, signal entropy, chaoticity and long-range temporal correlations. In addition, (They) estimated perturbational sensitivity using a global auditory oddball mismatch negativity (MMN) during meditation. >>

<< ️Relative to mindfulness, jhana was associated with pronounced self-reported sensory fading, slower respiration, higher neural signal diversity across multiple measures, reduced chaoticity, and enhanced MMN amplitude over frontocentral sites. Spectral analyses showed a flatter aperiodic one over f component and a frequency-specific reorganization of long-range temporal correlations. Together, increased diversity with reduced chaoticity and heightened deviance detection indicate a shift toward a metastable, near-critical regime during jhana. >>

<< ️(AA) propose an overlap of the phenomenology of jhana with minimal phenomenal experiences in terms of progressive attenuation of sensory content with preserved tonic alertness. Accordingly, (Their) findings suggest that criticality is a candidate neurophysiological marker of the absorptive, minimal-content dimension of the minimal phenomenal experience. >>

Jonas Mago, Joshua Brahinsky, Mark Miller, et al. Meditative absorption shifts brain dynamics toward criticality. arXiv: 2511.20990v1 [q-bio.NC]. Nov 26, 2025.

https://arxiv.org/abs/2511.20990

Also: brain, Zen, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, brain, Zen, criticality, transitions, meditation, meditative absorption, jhanas, breathing mindfulness.

# brain: self-organized learning emerges from coherent coupling of critical neurons.

<< ️Deep artificial neural networks have surpassed human-level performance across a diverse array of complex learning tasks, establishing themselves as indispensable tools in both social applications and scientific research. >>

<< ️Despite these advances, the underlying mechanisms of training in artificial neural networks remain elusive. >>

<< ️Here, (AA) propose that artificial neural networks function as adaptive, self-organizing information processing systems in which training is mediated by the coherent coupling of strongly activated, task-specific critical neurons. >>

<< ️(AA) demonstrate that such neuronal coupling gives rise to Hebbian-like neural correlation graphs, which undergo a dynamic, second-order connectivity phase transition during the initial stages of training. Concurrently, the connection weights among critical neurons are consistently reinforced while being simultaneously redistributed in a stochastic manner. >>

<< ️As a result, a precise balance of neuronal contributions is established, inducing a local concentration within the random loss landscape which provides theoretical explanation for generalization capacity. >>

<< ️(AA) further identify a later on convergence phase transition characterized by a phase boundary in hyperparameter space, driven by the nonequilibrium probability flux through weight space. The critical computational graphs resulting from coherent coupling also decode the predictive rules learned by artificial neural networks, drawing analogies to avalanche-like dynamics observed in biological neural circuits. >>

<< ️(AA) findings suggest that the coherent coupling of critical neurons and the ensuing local concentration within the loss landscapes may represent universal learning mechanisms shared by both artificial and biological neural computation. >>

Chuanbo Liu, Jin Wang. Self-organized learning emerges from coherent coupling of critical neurons. arXiv: 2509.00107v1 [cond-mat.dis-nn]. Aug 28, 2025.

https://arxiv.org/abs/2509.00107

Also: brain, neuro, network, random, transition, ai (artificial intell) (bot), in https://www.inkgmr.net/kwrds.html 

Keywords: gst, brain, neurons, networks, randomness, transitions, ai (artificial intell) (bot), learning mechanisms, self-organized learning, artificial neural networks, deep learning, neuronal coupling, criticality, stochasticity, avalanche-like dynamics.

# life: self-reinforcing cascades: a spreading model for beliefs or products of varying intensity or quality

<< ️Models of how things spread often assume that transmission mechanisms are fixed over time. However, social contagions—the spread of ideas, beliefs, innovations—can lose or gain in momentum as they spread: ideas can get reinforced, beliefs strengthened, products refined. >>

<< ️(AA) study the impacts of such self-reinforcement mechanisms in cascade dynamics. (They) use different mathematical modeling techniques to capture the recursive, yet changing nature of the process. >>

<< ️(AA) find a critical regime with a range of power-law cascade size distributions with nonuniversal scaling exponents. This regime clashes with classic models, where criticality requires fine-tuning at a precise critical point. Self-reinforced cascades produce critical-like behavior over a wide range of parameters, which may help explain the ubiquity of power-law distributions in empirical social data. >>

Laurent Hébert-Dufresne, Juniper Lovato, et al. Self-Reinforcing Cascades: A Spreading Model for Beliefs or Products of Varying Intensity or Quality. Phys. Rev. Lett. 135, 087401. Aug 21, 2025.

https://journals.aps.org/prl/abstract/10.1103/5mph-sws5

Also: behav, random, noise, walk, self-assembly, in https://www.inkgmr.net/kwrds.html 

Keywords: life, behavior, walk, random, random walks, noise, criticality, self-assembly, social contagions, self-reinforced cascades.

# gst: topologically nontrivial multicritical points.

<< ️Recently, the intriguing interplay between topology and quantum criticality has been unveiled in one-dimensional topological chains with extended nearest-neighbor couplings. In these systems, topologically distinct critical phases emerge with localized edge modes despite the vanishing bulk gap. >>

<< ️In this work, (AA) study the topological multicritical points at which distinct gapped and critical phases intersect. Specifically, (They) consider a topological chain with coupling up to the third nearest neighbors, which shows stable localized edge modes at the multicritical points. These points possess only nontrivial gapped and critical phases around them and are also characterized by the quadratic dispersion around the gap-closing points. >>

<< Further, (AA) analyze the nature of zeros in the vicinity of the multicritical points by calculating the discriminants of the associated polynomial. The discriminant uniquely identifies the topological multicritical points and distinguishes them from the trivial ones.  >>

AA << finally study the robustness of the zero-energy modes at the multicritical points at weak disorder strengths, and reveal the presence of a topologically nontrivial gapless Anderson-localized phase at strong disorder strengths. >>

Ranjith R Kumar, Pasquale Marra. Topologically nontrivial multicritical points. arXiv: 2507.11120v1 [cond-mat.dis-nn]. Jul 15, 2025.

https://arxiv.org/abs/2507.11120

Also: disorder & fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, disorder & fluctuations, criticality, multicritical points, transition.

# gst: apropos of ghost entities, criticality governs response dynamics and entrainment of periodically forced ghost cycles.

<< ️Many natural and engineered systems display oscillations that are characterized by multiple timescales. Typically, such systems are described as slow-fast systems, where the slow dynamics result from a hyperbolic slow manifold that guides the movement of the system's trajectories. Recently, (AA) have provided an alternative description in which the slow timescale results from Lyapunov-unstable transient dynamics of connected dynamical ghosts that form a closed orbit termed ghost cycle. >>

Here, AA << investigate the response properties of both types of systems to external forcing. Using the classical Van der Pol oscillator and modified versions of this model that correspond to a one-ghost and a two-ghost cycle, respectively, (They) find significant differences in the responses of slow-fast systems and ghost cycles, including increased entrainment regions of the latter. Nonautonomous model analysis reveals that the differences stem from a continuous remodeling of the attractor landscape of the ghost cycle models, enabled by being organized close to saddle-node on invariant cycle bifurcations, in contrast to a qualitatively unaltered attractor landscape of the slow-fast system. >>

(AA) << ️further demonstrate that the observed features occur in various systems with ghost cycles regardless of the exact mathematical model formulation leading to those ghost cycles, making them likely to apply to many other models with ghost cycles across different disciplines and contexts. (They) thus propose that systems containing ghost cycles display increased flexibility and responsiveness to continuous environmental changes. >>

Daniel Koch, Ulrike Feudel, Aneta Koseska. Criticality governs response dynamics and entrainment of periodically forced ghost cycles. Phys. Rev. E 112, 014205. Jul 8, 2025.

https://journals.aps.org/pre/abstract/10.1103/3d9z-qrb1

Also: transition, attractor, self-assembly, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transition, attractor, self-assembly, bifurcations, saddle-node, synchronization, criticality, self-organized criticality.

# gst: nonstationary critical phenomena: expanding the critical point.

<< A prototypical model of symmetry-broken active matter -- biased quorum-sensing active particles (bQSAPs) -- is used to extend notions of dynamic critical phenomena to the paradigmatic setting of driven transport, where characteristic behaviours are nonstationary and involve persistent fluxes. >>

<< To do so, (AA) construct an effective field theory with a single order-parameter -- a nonstationary analogue of active Model B -- that reflects the fact that different properties of bQSAPs can only be interpreted in terms of passive thermodynamics in appropriately chosen inertial frames. This codifies the movement of phase boundaries due to nonequilibrium fluxes between coexisting bulk phases in terms of a difference in effective chemical potentials and therefore an 'unequal' tangent construction on a bulk free energy density. >>

<< The result is both an anomalous form of coarsening and, more generally, an exotic phase structure; binodals are permitted to cross spinodal lines so that criticality is no longer constrained to a single point. >>

<< Instead, criticality, with exponents that are seemingly unchanged from symmetric QSAPs, is shown to exist along a line that marks the entry to an otherwise forbidden region of phase space. The interior of this region is not critical in the conventional sense, but retains certain features of criticality, which (AA) term pseudo-critical. >>

<< Whilst an inability to satisfy a Ginzburg criterion implies that fluctuations remain relevant at macroscopic scales, finite-wavenumber fluctuations grow at finite rates and exhibit non-trivial dispersion relations. The interplay between the growth of fluctuations and the speed at which they move relative to the bulk results in distinct regimes of micro- and meso-phase separation. >>

Richard E. Spinney, Richard G. Morris. Nonstationary critical phenomena: expanding the critical point. Phys. Rev. E 111, 064129. Jun 23, 2025.

https://journals.aps.org/pre/abstract/10.1103/hx6n-9qsk

arXiv: 2412.15627v2 [cond-mat.stat-mech]. Jun 25, 2025. 

https://arxiv.org/abs/2412.15627

Also: particle, disorder & fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, active particles, disorder & fluctuations, criticality, pseudo-criticality, transitions.

# gst: topological phase transition under infinite randomness

<< In clean and weakly disordered systems, topological and trivial phases having a finite bulk energy gap can transit to each other via a quantum critical point. In presence of strong disorder, both the nature of the phases and the associated criticality can fundamentally change. >>

Here AA << investigate topological properties of a strongly disordered fermionic chain where the bond couplings are drawn from normal probability distributions which are defined by characteristic standard deviations. Using numerical strong disorder renormalization group methods along with analytical techniques, (AA) show that the competition between fluctuation scales renders both the trivial and topological phases gapless with Griffiths like rare regions. >>

<< Moreover, the transition between these phases is solely governed by the fluctuation scales, rather than the means, rendering the critical behavior to be determined by an infinite randomness fixed point with an irrational central charge. (AA) work points to a host of novel topological phases and atypical topological phase transitions which can be realized in systems under strong disorder. >>

Saikat Mondal, Adhip Agarwala. Topological Phase Transition under Infinite Randomness. arXiv: 2506.19913v1 [cond-mat.dis-nn]. Jun 24, 2025.

https://arxiv.org/abs/2506.19913

Also: order, disorder, disorder & fluctuations, random, transition, forms of power, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, order, disorder, disorder & fluctuations, randomness, criticality, transitions, forms of power

FonT: who knows if during some master's courses on the organization and evolution of social enclosures, held by the legendary "Frattocchie School" ( https://it.m.wikipedia.org/wiki/Scuola_delle_Frattocchie ) during the early 80s (but also early 90s) some bizarre theoretician advanced the imaginative, up in the air, absolutely unfounded hypothesis (here it is emphasized: absolutely), about the possibility of an immediate cracking of a social structure due to the action of idiots (?) disguised as idiots until the complete, universal, ontheback breakthrough anzicheforse?

# gst: random interaction in active matter models; critical changes in Vicsek's scenario.

<< Randomness plays a key role in the order transition of active matter but has not yet been explicitly considered in pairwise interaction connection. In this paper, (AA) introduce the perception rate 𝑃 into the Vicsek model as the probability of the interaction connections and model the connections as superposition states. (They) show that with increasing 𝑃, the polar order number undergoes an order transition and then saturation. >>

<< The order transition is a first-order phase transition with band formation, and the effect of 𝑃 is different from density. The change of the order number is linked with the interaction structure. The order transition, order saturation, and phase separation correspond to different critical changes in the local interaction number. >>

<< The global interaction structure is further analyzed as a network. The decrease of 𝑃 is comparable to random edge removal, under which the network experiences modal transitions near the critical points of the order number, and the network exhibits surprising robustness.  (AA) results suggest that random interaction can be a new important factor in active matter models, with potential applications in robotic swarms and social activities. >>

Ruizhi Jin, Kejun Dong. Role of random interaction connection in the order transition of active matter based on the Vicsek model. Phys. Rev. E 111, 064122. Jun 17, 2025.

https://journals.aps.org/pre/abstract/10.1103/9rdd-tbn7

arXiv: 2501.10669v1 [cond-mat.soft]. Jan 18, 2025. 

https://arxiv.org/abs/2501.10669

Also: network, random, perception, transition, swarm, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, active matter, network, randomness, perception, criticality, transitions, swarm.

# gst: interactive anisotropic walks in 2D generated from a 3-state opinion dynamics model.

<< A system of interacting walkers is considered in a two-dimensional hypothetical space, where the dynamics of each walker are governed by the opinion states of the agents of a fully connected three-state opinion dynamics model. Such walks, studied in different models of statistical physics, are usually considered in one-dimensional virtual spaces. >>

In this article AA has performed the mapping << in such a way that the walk is directed along the 𝑌 axis while it can move either way along the 𝑋 axis. The walk shows that there are three distinct regions as the noise parameter, responsible for driving a continuous phase transition in the model, is varied. In absence of any noise, the scaling properties and the form of the distribution along either axis do not follow any conventional form. >>

<< For any finite noise below the critical point the bivariate distribution of the displacements is found to be a modified biased Gaussian function while above it, only the marginal distribution along one direction is Gaussian. The marginal probability distributions can be extracted and the scaling forms of different quantities, showing power-law behavior, are obtained. The directed nature of the walk is reflected in the marginal distributions as well as in the exponents. >>

Surajit Saha, Parongama Sen. Interactive anisotropic walks in two dimensions generated from a three-state opinion dynamics model. Phys. Rev. E 111, 064123. Jun 18, 2025.

https://journals.aps.org/pre/abstract/10.1103/5c2y-yj1z

arXiv: 2409.10413v3 [cond-mat.stat-mech]. Apr 28, 2025. 

https://arxiv.org/abs/2409.10413

Also: walk, noise, random, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, walk, walking, random walk, randomness, noise, transitions, noise-induced transitions, criticality.

# gst: early warning skill, extrapolation and tipping for accelerating cascades; if the upstream system crosses a tipping point, this can shorten the timescale of valid extrapolation.

AA << investigate how nonlinear behaviour (both of forcing in time and of the system itself) can affect the skill of early warning signals to predict tipping in (directionally) coupled bistable systems when using measures based on critical slowing down due to the breakdown of extrapolation. (They) quantify the skill of early warnings with a time horizon using a receiver-operator methodology for ensembles where noise realisations and parameters are varied to explore the role of extrapolation and how it can break down. >>

AA << highlight cases where this can occur in an accelerating cascade of tipping elements, where very slow forcing of a slowly evolving ``upstream'' system forces a more rapidly evolving ``downstream'' system. If the upstream system crosses a tipping point, this can shorten the timescale of valid extrapolation. >>

<< In particular, ``downstream-within-upstream'' tipping will typically have warnings only on a timescale comparable to the duration of the upstream tipping process, rather than the timescale of the original forcing. >>

Peter Ashwin, Robbin Bastiaansen, et al. Early warning skill, extrapolation and tipping for accelerating cascades.arXiv: 2506.01981v1 [nlin.CD]. May 16, 2025.

https://arxiv.org/abs/2506.01981

Also: crack, fracture, noise, track changes in noise, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, climate, early warning, tipping prediction, accelerating cascade, crossing a tipping point, multiple tipping points, fragmented tipping, criticality, noise, noise-induced tipping, crack, fracture