Discontinuous Phase Transition Research Articles

Enhancing predictive accuracy in social contagion dynamics via directed hypergraph structures

Evidence from both theoretical and empirical studies suggests that higher-order networks have emerged as powerful tools for modeling social contagions, such as opinion formation. In this article, we develop a model of social contagion on directed hypergraphs by considering the heterogeneity of individuals and environments in terms of reinforcing contagion effects. By distinguishing the directedness between nodes and hyperedges, we find that the bistable interval of the discontinuous phase transition decreases as the directedness strength decreases. Additionally, directed hypergraphs tend to generate bistable intervals when nodes with a large hyperdegree are more likely to adopt a specific opinion, as evidenced by simulations of directionality assignments for three sets of real networks. These findings provide two approaches to enhance the accuracy of predicting social contagion dynamics: one is to increase the stubbornness of all individuals, and the other is to prioritize increasing the stubbornness of highly influential individuals.

Quantifying the impacts of Canadian wildfires on regional air pollution networks

Wildfire smoke greatly impacts regional atmospheric systems, causing changes in the behavior of pollution. However, the impacts of wildfire smoke on pollution behavior are not easily quantifiable due to the complex nature of atmospheric systems. Air pollution correlation networks have been used to quantify air pollution behavior during ambient conditions. However, it is unknown how extreme pollution events impact these networks. Therefore, we propose a multidimensional air pollution correlation network framework to quantify the impacts of wildfires on air pollution behavior. The impacts are quantified by comparing two time periods, one during the 2023 Canadian wildfires and one during normal conditions with two complex network types for each period. In this study, the value network represents PM2.5 concentrations and the rate network represents the rate of change of PM2.5 concentrations. Wildfires' impacts on air pollution behavior are captured by structural changes in the networks. The wildfires caused a discontinuous phase transition during percolation in both network types which represents non-random organization of the most significant spatiotemporal correlations. Additionally, wildfires caused changes to the connectivity of stations leading to more interconnected networks with different influential stations. During the wildfire period, highly polluted areas are more likely to form connections in the network, quantified by an 86 % and 19 % increase in the connectivity of the value and rate networks respectively compared to the normal period. In this study, we create novel understandings of the impacts of wildfires on air pollution correlation networks, show how our method can create important insights into air pollution patterns, and discuss potential applications of our methodologies. This study aims to enhance capabilities for wildfire smoke exposure mitigation and response strategies.

Catastrophic cascade of failures in interdependent hypergraphs.

The failures of individual agents can significantly impact the functionality of associated groups in interconnected systems. To reveal these impacts, we develop a threshold model to investigate cascading failures in double-layer hypergraphs with interlayer interdependence. We hypothesize that a hyperedge disintegrates when the proportion of failed nodes within it exceeds a threshold. Due to the interdependence between a node and its replica in the other layer, the disintegrations of these hyperedges could trigger a cascade of events, leading to an iterative collapse across these two layers. We find that double-layer hypergraphs undergo abrupt, discontinuous first-order phase transitions during systemic collapse regardless of the specific threshold value. Additionally, the connectivity measured by average cardinality and hyperdegree plays a crucial role in shaping system robustness. A higher average hyperdegree always strengthens system robustness. However, the relationship between system robustness and average cardinality exhibits non-monotonic behaviors. Specifically, both excessively small and large average cardinalities undermine system robustness. Furthermore, a higher threshold value can boost the system's robustness. In summary, our study provides valuable insights into cascading failure dynamics in double-layer hypergraphs and has practical implications for enhancing the robustness of complex interdependent systems across domains.

Discontinuous phase transition from ferromagnetic to oscillating states in a nonequilibrium mean-field spin model.

We study a nonequilibrium ferromagnetic mean-field spin model exhibiting a phase with spontaneous temporal oscillations of the magnetization, on top of the usual paramagnetic and ferromagnetic phases. This behavior is obtained by introducing dynamic field variables coupled to the spins through nonreciprocal couplings. We determine a nonequilibrium generalization of the Landau free energy in terms of the large deviation function of the magnetization and of an appropriately defined smoothed stochastic time derivative of the magnetization. While the transition between paramagnetic and oscillating phase is continuous, the transition between ferromagnetic and oscillating phases is found to be discontinuous, with a coexistence of both phases, one being stable and the other one metastable. Depending on parameter values, the ferromagnetic points may either be inside or outside the limit cycle, leading to different transition scenarios. The stability of these steady states is determined from the large deviation function. We also show that in the coexistence region, the entropy production has a pronounced maximum as a function of system size.

Filtering induced explosive death in coupled FitzHugh–Nagumo neurons: Theory and experiment

Explosive emergent behavior governed by discontinuous and irreversible phase transition is in the center of recent research. In this paper we show that explosive amplitude death (AD) can be induced in a system of coupled oscillators if diffusion is accompanied by low-pass filtering in the mutual coupling path. Here we consider a ring network of diffusively coupled FitzHugh–Nagumo oscillators, and through theoretical and experimental investigations explore how the low-pass filter induces and controls the transition to explosive AD state. We derive the conditions of getting AD in the network through linear stability analysis. Using one and two parameter bifurcation analysis we find the explicit parametric zone of explosive death in the limiting case of two neurons, which reveals that the explosive death arises through the saddle–node bifurcation of limit cycle. In the strong coupling limit, we observe an interesting semi-explosive death scenario, where both continuous and discontinuous transitions are present. Finally, using electronic hardware circuits, we demonstrate the first experimental observation of explosive amplitude death that establishes the robustness of the scenario in a practical setup.

Structural dynamics at surfaces by ultrafast reflection high-energy electron diffraction.

Many fundamental processes of structural changes at surfaces occur on a pico- or femtosecond timescale. In order to study such ultrafast processes, we have combined modern surface science techniques with fs-laser pulses in a pump-probe scheme. Grazing incidence of the electrons ensures surface sensitivity in ultrafast reflection high-energy electron diffraction (URHEED). Utilizing the Debye-Waller effect, we studied the nanoscale heat transport from an ultrathin film through a hetero-interface or the damping of vibrational excitations in monolayer adsorbate systems on the lower ps-timescale. By means of spot profile analysis, the different cooling rates of epitaxial Ge nanostructures of different size and strain state were determined. The excitation and relaxation dynamics of a driven phase transition far away from thermal equilibrium is demonstrated using the In-induced (8 × 2) reconstruction on Si(111). This Peierls-distorted surface charge density wave system exhibits a discontinuous phase transition of first order at 130 K from a (8 × 2) insulating ground state to (4 × 1) metallic excited state. Upon excitation by a fs-laser pulse, this structural phase transition is non-thermally driven in only 700 fs into the excited state. A small barrier of 40 meV hinders the immediate recovery of the ground state, and the system is found in a metastable supercooled state for up to few nanoseconds.

SAR dynamical mechanism affected by diminishing marginal effect based on personal fashion psychology on multi-layer contacted network

People in complex systems exhibit varying capacities for social interaction because of differences in personal psychology, educational attainment, and social class. It is true that people often use different social networks and show different enthusiasm for obtaining information, but their interest in collecting information will decrease over time. Our study on Personal Fashion Psychology (PFP) has shown that when people get information, they behave in a way known as the Diminishing Marginal Effect (DME-PFP behavior). Next, we created a SAR propagation dynamics model on a multi-layer contact network to represent DME-PFP behavior using a threshold function. Then, to assess and uncover the transmission mechanism of individual behaviour, we use partition theory. A boundary phenomena is displayed by the propagation mode, as demonstrated by both theoretical analysis and simulated tests. The final size can exhibit either discontinuous first-order phase transitions or continuous second-order phase changes in individual DME-PFP behaviour. Meanwhile, through the unit transmission probability changed, the ideal DME-PFP parameters occur at the largest final adoption size. Moreover, the promotion of the propagation pattern and behaviour from continuous second-order to discontinuous first-order is facilitated by interpersonal contact. The numerical analysis and the actual models may eventually agree.

Approximate master equationsfor the spatial public goods game.

The spatial public goods game has been used to examine factors that promote cooperation. Owing to the complexity of the dynamics of this game, previous studies on this model neglected analytical approaches and relied entirely on numerical calculations using the Monte Carlo (MC) simulations. In this paper, we present the approximate master equations(AMEs) for this model. We report that the results obtained by the AMEs are mostly qualitatively consistent with those obtained by the MC simulations. Furthermore, we show that it is possible to obtain phase boundaries analytically in certain parameter regions. In the region where the noise in strategy decisions is very large, the phase boundary can be obtained analytically by considering perturbations from the steady state of the voter model. In the noiseless region, discontinuous phase transitions occur because of the characteristics of the function that represents strategy updating. Our approach is useful for clarifying the details of the mechanisms that promote cooperation and can be easily applied to other group interaction models.

Discontinuous phase transition switching induced by a power-law function between dynamical parameters in coupled oscillators

In biological or physical systems, the intrinsic properties of oscillators are heterogeneous and correlated. These two characteristics have been empirically validated and have garnered attention in theoretical studies. In this paper, we propose a power-law function existed between the dynamical parameters of the coupled oscillators, which can control discontinuous phase transition switching. Unlike the special designs for the coupling terms, this generalized function within the dynamical term reveals another path for generating the first-order phase transitions. The power-law relationship between dynamic characteristics is reasonable, as observed in empirical studies, such as long-term tremor activity during volcanic eruptions and ion channel characteristics of the Xenopus expression system. Our work expands the conditions that used to be strict for the occurrence of the first-order phase transitions and deepens our understanding of the impact of correlation between intrinsic parameters on phase transitions. We explain the reason why the continuous phase transition switches to the discontinuous phase transition when the control parameter is at a critical value.

Supercriticality, Glassy Dynamics, and the New Insight into Melting/Freezing Discontinuous Transition in Linseed Oil

The long-range supercritical changes of dielectric constant, resembling ones observed in the isotropic liquid phase of liquid crystalline compounds, are evidenced for linseed oil—although in the given case, the phenomenon is associated with the liquid–solid melting/freezing discontinuous phase transitions. This ‘supercriticality’ can be an additional factor supporting the unique pro-health properties of linseed oil. Broadband dielectric spectroscopy studies also revealed the ‘glassy’ changes of relaxation times, well portrayed by the ‘activated and critical’ equation recently introduced. In the solid phase, the premelting effect characteristic for the canonic melting/freezing discontinuous transition, i.e., without any pretransitional effect in the liquid phase, has been detected. It is interpreted within the grain model, and its parameterization is possible using the Lipovsky model and the ‘reversed’ Mossotti catastrophe concept. For the premelting effect in the solid state, the singular ‘critical’ temperature correlates with the bulk discontinuous melting and freezing temperatures. Consequently, the report shows that linseed oil, despite its ‘natural and complex’ origins, can be considered a unique model system for two fundamental problems: (i) pretransitional (supercritical) effects in the liquid state associated with a weakly discontinuous phase transition, and (ii) the premelting behavior in the solid side of the discontinuous melting/freezing discontinuous transition.

Coupled propagation dynamics on complex networks: A brief review

Coupled propagation dynamics based on complex networks have received widespread attention in recent years. This work reviews the research work related to coupling propagation dynamics on single-layer complex networks, multi-layer complex networks and high-order complex networks. We sort out relevant research results from three aspects: competitive propagation, cooperative propagation and asymmetric coupled propagation, finding that different coupling mechanisms focus on different dynamic properties. The dynamic characteristics such as coexistence threshold in competitive propagation, discontinuous phase transition in cooperative propagation, outbreak threshold and propagation prevalence in asymmetric coupling propagation have been extensively discussed. We conclude by giving some valuable future research topics in coupled propagation dynamics.

Study on phase transition critical phenomena in group movement based on eigen microstate theory

Group motion exists widely in nature. Physicists use abstract models, such as the Vicsek model, to simplify group motion to obtain universal laws. However, the order parameters and phase transition types that describe the characteristics of the Vicsek model system are still controversial. For example, how to characterize the order parameters and types of phase transitions that characterize the system. This paper starts with the eigen microstate method and studies the Vicsek model. First, the continuous phase transition in the system is deeply studied through scaling analysis, and two critical exponents about the noise are obtained. Second, considering the density effect, similar to the noise study, three eigen microstates in the Vicsek model are revealed through scaling analysis, showing discontinuous and continuous phase transitions. Moreover, it is proved that in the actual infinite system, continuous phase transition and discontinuous phase transition still exist. Finally, the experimental data under different noises and densities are obtained through a large number of numerical simulations, and the phase diagram of the Vicsek model is depicted.

Phase transition phenomena in social propagation with dynamic fashion tendency and individual contact

In complex systems, individuals exhibit various social contact capacities on account of differences in societal strata, educational backgrounds, and individual psychology. It is a fact that people tend to utilize diverse social networks and demonstrate ever-changing fashion trends. From our study on personal psychology, we have noted that individuals display a behaviour known as dynamic fashion tendency (DFT) when receiving information. Next, to represent DFT behaviour through a threshold model, we devised a dynamic SAR propagation model on a multi-layer contact network. For the transmission mechanism of individual behaviour, we utilized partition theory to investigate and uncover. Both theoretical analysis and simulation experiments demonstrate that the propagation mode exhibits a boundary phenomenon. The final adoption size may demonstrate either continuous second-order or discontinuous first-order phase transitions, depending on individual DFT behaviour. When unit propagation probability is constant, the largest final adoption size is attained with the ideal DFT parameters. Additionally, personal contact plays a role in spreading behaviour and shifting the propagation pattern from continuous second-order to discontinuous first-order. Ultimately, numerical analysis can correspond with real models.

About the de Almeida–Thouless line in neural networks

In this work we present a rigorous and straightforward method to detect the onset of the instability of replica-symmetric theories in information processing systems, which does not require a full replica analysis as in the method originally proposed by de Almeida and Thouless for spin glasses. The method is based on an expansion of the free-energy obtained within one-step of replica symmetry breaking (RSB) around the RS value. As such, it requires solely continuity and differentiability of the free-energy and it is robust to be applied broadly to systems with quenched disorder. We apply the method to the Hopfield model and to neural networks with multi-node Hebbian interactions, as case studies. In the appendices we test the method on the Sherrington–Kirkpatrick and the Ising P-spin models, recovering the AT lines known in the literature for these models, as a special limit, which corresponds to assuming that the transition from the RS to the RSB phase can be obtained by varying continuously the order parameters. Our method provides a generalization of the AT approach, which does not rely on this limit and can be applied to systems with discontinuous phase transitions, as we show explicitly for the spherical P-spin model, recovering the known RS instability line.

How does a hyperuniform fluid freeze?

All phase transitions can be categorized into two different types: continuous and discontinuous phase transitions. Discontinuous phase transitions are normally accompanied with significant structural changes, and nearly all of them have the kinetic pathway of nucleation and growth, if the system does not suffer from glassy dynamics. Here, in a system of barrier-controlled reactive particles, we find that the discontinuous freezing transition of a nonequilibrium hyperuniform fluid into an absorbing state does not have the kinetic pathway of nucleation and growth, and the transition is triggered by long-wavelength fluctuations. The transition rate decreases with increasing the system size, which suggests that the metastable hyperuniform fluid could be kinetically stable in an infinitely large system. This challenges the common understanding of metastability in discontinuous phase transitions. Moreover, we find that the "metastable yet kinetically stable" hyperuniform fluid features a scaling in the structure factor [Formula: see text] in 2D, which is the third dynamic hyperuniform state in addition to the critical hyperuniform state with [Formula: see text] and the nonequilibrium hyperuniform fluid with [Formula: see text].

Long-Range Order for Critical Book-Ising and Book-Percolation

In this paper, we investigate the behaviour of statistical physics models on a book with pages that are isomorphic to half-planes. We show that even for models undergoing a continuous phase transition on Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}^2$$\\end{document}, the phase transition becomes discontinuous as soon as the number of pages is sufficiently large. In particular, we prove that the Ising model on a three pages book has a discontinuous phase transition (if one allows oneself to consider large coupling constants along the line on which pages are glued). Our work confirms predictions in theoretical physics which relied on renormalization group, conformal field theory and numerics (Cardy in J Phys A Math Gen 24(22):L131, 1991; Iglói et al. in J Phys A Math Gen 24(17):L1031, 1991; Stéphan et al. in Phys Rev B 82(12):125455, 2010) some of which were motivated by the analysis of the Renyi entropy of certain quantum spin systems.

Cascading failures in interdependent networks with reinforced crucial nodes and dependency groups

Previous studies of group percolation models in interdependent networks with reinforced nodes have rarely addressed the effects of the degree of reinforced nodes and the heterogeneity of group size distribution. In this paper, a cascading failure model in interdependent networks with reinforced crucial nodes and dependency groups is investigated numerically and analytically. For each group, we assume that if all the nodes in a group fail on one network, a node on another network that depends on that group will fail. We find that rich percolation transitions can be classified into three types: discontinuous, continuous, and hybrid phase transitions, which depend on the density of reinforced crucial nodes, the group size, and the heterogeneity of group size distribution. Importantly, our proposed crucial reinforced method has higher reinforcement efficiency than the random reinforced method. More significantly, we develop a general theoretical framework to calculate the percolation transition points and the shift point of percolation types. Simulation results show that the robustness of interdependent networks can be improved by increasing the density of reinforced crucial nodes, the group size, and the heterogeneity of group size distribution. Our theoretical results can well agree with numerical simulations. These findings might develop a new perspective for designing more resilient interdependent infrastructure networks.

Critical-like Brain Dynamics in a Continuum from Second- to First-Order Phase Transition.

The classic brain criticality hypothesis postulates that the brain benefits from operating near a continuous second-order phase transition. Slow feedback regulation of neuronal activity could, however, lead to a discontinuous first-order transition and thereby bistable activity. Observations of bistability in awake brain activity have nonetheless remained scarce and its functional significance unclear. Moreover, there is no empirical evidence to support the hypothesis that the human brain could flexibly operate near either a first- or second-order phase transition despite such a continuum being common in models. Here, using computational modeling, we found bistable synchronization dynamics to emerge through elevated positive feedback and occur exclusively in a regimen of critical-like dynamics. We then assessed bistability in vivo with resting-state MEG in healthy adults (7 females, 11 males) and stereo-electroencephalography in epilepsy patients (28 females, 36 males). This analysis revealed that a large fraction of the neocortices exhibited varying degrees of bistability in neuronal oscillations from 3 to 200 Hz. In line with our modeling results, the neuronal bistability was positively correlated with classic assessment of brain criticality across narrow-band frequencies. Excessive bistability was predictive of epileptic pathophysiology in the patients, whereas moderate bistability was positively correlated with task performance in the healthy subjects. These empirical findings thus reveal the human brain as a one-of-a-kind complex system that exhibits critical-like dynamics in a continuum between continuous and discontinuous phase transitions.SIGNIFICANCE STATEMENT In the model, while synchrony per se was controlled by connectivity, increasing positive local feedback led to gradually emerging bistable synchrony with scale-free dynamics, suggesting a continuum between second- and first-order phase transitions in synchrony dynamics inside a critical-like regimen. In resting-state MEG and SEEG, bistability of ongoing neuronal oscillations was pervasive across brain areas and frequency bands and was observed only with concurring critical-like dynamics as the modeling predicted. As evidence for functional relevance, moderate bistability was positively correlated with executive functioning in the healthy subjects, and excessive bistability was associated with epileptic pathophysiology. These findings show that critical-like neuronal dynamics in vivo involves both continuous and discontinuous phase transitions in a frequency-, neuroanatomy-, and state-dependent manner.

Learning by confusion approach to identification of discontinuous phase transitions.

Recently, the learning by confusion (LbC) approach has been proposed as a machine learning tool to determine the critical temperature T_{c} of phase transitions without any prior knowledge of its even approximate value. The method has been proven effective, but it has been used only for continuous phase transitions, where the confusion results only from deliberate incorrect labeling of the data. However, in the case of a discontinuous phase transition, additional confusion can result from the coexistence of different phases. To verify whether the confusion scheme can also be used for discontinuous phase transitions, we apply the LbC method to three microscopic models, the Blume-Capel, the q-state Potts, and the Falicov-Kimball models, which undergo continuous or discontinuous phase transitions depending on model parameters. With the help of a simple model, we predict that the phase coexistence present in discontinuous phase transitions can indeed make the neural network more confused and thus decrease its performance. However, numerical calculations performed for the models mentioned above indicate that other aspects of this kind of phase transition are more important and can render the LbC method even less effective. Nevertheless, we demonstrate that in some cases the same aspects allow us to use the LbC method to identify the order of a phase transition.

Impact of peer pressure on the evolution of cooperation in prisoner’s dilemma game

Assuming that cooperators and defectors are influenced by peer pressure with a certain probability. The influence mode is that the neighbors who adopts the opposite strategy to the central individual will reduce the fitness of the central individual. This paper explores the impact of peer pressure on the evolution of cooperation in the prisoner’s dilemma game under the condition that the pressure sensitivity of the cooperators and defectors are equal and unequal. The simulation results show that peer pressure can promote cooperation. When the pressure sensitivity of the cooperators and defectors are equal, the influence of pressure sensitivity on the system is non-trivial. According to the value of pressure intensity, evolution of the system can be roughly divided into three categories. When the pressure intensity is weak, the system is not affected by pressure sensitivity and remains in a state of full defection. When the pressure intensity is moderate, the system undergoes a continuous phase transition from full defection to coexistence and then to full cooperation with the increase of the pressure sensitivity. When the pressure intensity is high, the system undergoes a discontinuous phase transition from full defection to full cooperation and even to full defection with the increase of the pressure sensitivity. In addition, when cooperators and defectors have different pressure sensitivities, the cooperation promotion effect is better than that when cooperators and defectors have the same pressure sensitivities. Specifically, cooperation can be promoted or even dominated under lower pressure sensitivity and pressure intensity, which can explain the emergence of cooperation.