Absorbing-state Phase Transition Research Articles

The role of mobility in epidemics near criticality

Abstract The general epidemic process (GEP), also known as susceptible-infected-recovered model, provides a minimal model of how an epidemic spreads within a population of susceptible individuals who acquire permanent immunization upon recovery. This model exhibits a second-order absorbing state phase transition, commonly studied assuming immobile healthy individuals. We investigate the impact of mobility on the scaling properties of disease spreading near the extinction threshold by introducing two generalizations of GEP, where the mobility of susceptible and recovered individuals is examined independently. In both cases, including mobility violates GEP’s rapidity reversal symmetry and alters the number of absorbing states. The critical dynamics of the models are analyzed through a perturbative renormalization group (RG) approach and large-scale stochastic simulations using a Gillespie algorithm. The RG analysis predicts both models to belong to the same novel universality class describing the critical dynamics of epidemic spreading when the infected individuals interact with a diffusive species and gain immunization upon recovery. At the associated RG fixed point, the immobile species decouples from the dynamics of the infected species, dominated by the coupling with the diffusive species. Numerical simulations in two dimensions affirm our RG results by identifying the same set of critical exponents for both models. Violation of the rapidity reversal symmetry is confirmed by breaking the associated hyperscaling relation. Our study underscores the significance of mobility in shaping population spreading dynamics near the extinction threshold.

Quantum reaction-limited reaction–diffusion dynamics of noninteracting Bose gases

We investigate quantum reaction–diffusion (RD) systems in one-dimension with bosonic particles that coherently hop in a lattice, and when brought in range react dissipatively. Such reactions involve binary annihilation ( A+A→∅ ) and coagulation ( A+A→A ) of particles at distance d. We consider the reaction-limited regime, where dissipative reactions take place at a rate that is small compared to that of coherent hopping. In classical RD systems, this regime is correctly captured by the mean-field approximation. In quantum RD systems, for noninteracting fermionic systems, the reaction-limited regime recently attracted considerable attention because it has been shown to give universal power law decay beyond mean field for the density of particles as a function of time. Here, we address the question whether such universal behavior is present also in the case of the noninteracting Bose gas. We show that beyond mean-field density decay for bosons is possible only for reactions that allow for destructive interference of different decay channels. Furthermore, we study an absorbing-state phase transition induced by the competition between branching A→A+A , decay A→∅ and coagulation A+A→A . We find a stationary phase-diagram, where a first and a second-order transition line meet at a bicritical point which is described by tricritical directed percolation. These results show that quantum statistics significantly impact on both the stationary and the dynamical universal behavior of quantum RD systems.

Absorbing state phase transition with Clifford circuits

The role of quantum fluctuations in modifying the critical behavior of nonequilibrium phase transitions is a fundamental but unsolved question. In this study, we examine the absorbing state phase transition of a 1D chain of qubits undergoing a contact process that involves both coherent and classical dynamics. We adopt a discrete-time quantum model with states that can be described in the stabilizer formalism, and therefore allows for an efficient simulation of large system sizes. The extracted critical exponents indicate that the absorbing state phase transition of this Clifford circuit model belongs to the directed percolation universality class. This suggests that the inclusion of quantum fluctuations does not necessarily alter the critical behavior of nonequilibrium phase transitions of purely classical systems. Finally, we extend our analysis to a non-Clifford circuit model, where a tentative scaling analysis in small systems reveals critical exponents that are also consistent with the directed percolation universality class. Published by the American Physical Society 2024

Griffiths phase in a facilitated Rydberg gas at low temperatures

The spread of excitations by Rydberg facilitation bears many similarities to epidemics. Such systems can be modeled with Monte Carlo simulations of classical rate equations to great accuracy as a result of high dephasing. Motivated by experiments, we theoretically analyze the dynamics of a Rydberg many-body system in the facilitation regime in the limits of high and low temperatures. In the high-temperature limit, a homogeneous mean-field behavior is recovered, while characteristic effects of heterogeneity can be seen in a frozen gas. At high temperatures, the system displays an absorbing-state phase transition and, in the presence of an additional loss channel, self-organized criticality. In a frozen or low-temperature gas, excitations are constrained to a network resembling an Erdős-Rényi graph. We show that the absorbing-state phase transition is replaced with an extended Griffiths phase, which we accurately describe by a susceptible-infected-susceptible model on the Erdős-Rényi network taking into account Rydberg blockade. Published by the American Physical Society 2024

Controlling Entanglement at Absorbing State Phase Transitions in Random Circuits.

Many-body unitary dynamics interspersed with repeated measurements display a rich phenomenology hallmarked by measurement-induced phase transitions. Employing feedback-control operations that steer the dynamics toward an absorbing state, we study the entanglement entropy behavior at the absorbing state phase transition. For short-range control operations, we observe a transition between phases with distinct subextensive scalings of entanglement entropy. In contrast, the system undergoes a transition between volume-law and area-law phases for long-range feedback operations. The fluctuations of entanglement entropy and of the order parameter of the absorbing state transition are fully coupled for sufficiently strongly entangling feedback operations. In that case, entanglement entropy inherits the universal dynamics of the absorbing state transition. This is, however, not the case for arbitrary control operations, and the two transitions are generally distinct. We quantitatively support our results by introducing a framework based on stabilizer circuits with classical flag labels. Our results shed new light on the problem of observability of measurement-induced phase transitions.

Self-organized criticality in a mesoscopic model of excitatory-inhibitory neuronal populations by short-term and long-term synaptic plasticity.

Dynamics of an interconnected population of excitatory and inhibitory spiking neurons wandering around a Bogdanov-Takens (BT) bifurcation point can generate the observed scale-free avalanches at the population level and the highly variable spike patterns of individual neurons. These characteristics match experimental findings for spontaneous intrinsic activity in the brain. In this paper, we address the mechanisms causing the system to get and remain near this BT point. We propose an effective stochastic neural field model which captures the dynamics of the mean-field model. We show how the network tunes itself through local long-term synaptic plasticity by STDP and short-term synaptic depression to be close to this bifurcation point. The mesoscopic model that we derive matches the directed percolation model at the absorbing state phase transition.

Contact process with simultaneous spatial and temporal disorder

We study the absorbing-state phase transition in the one-dimensional contact process under the combined influence of spatial and temporal random disorders. We focus on situations in which the spatial and temporal disorders decouple. Couched in the language of epidemic spreading, this means that some spatial regions are, at all times, more favorable than others for infections, and some time periods are more favorable than others independent of spatial location. We employ a generalized Harris criterion to discuss the stability of the directed percolation universality class against such disorder. We then perform large-scale Monte Carlo simulations to analyze the critical behavior in detail. We also discuss how the Griffiths singularities that accompany the nonequilibrium phase transition are affected by the simultaneous presence of both disorders.

Contact process on weighted planar stochastic lattice

We study the absorbing state phase transition in the contact process on the weighted planar stochastic (WPS) lattice. The WPS lattice is multifractal. Its dual network has a power-law degree distribution function and is also embedded in a bidimensional space. Moreover, it represents a novel way to introduce coordination disorder in lattice models. We investigated the critical behavior of the disordered system using extensive simulations. Our results show the critical behavior is distinct from that on a regular lattice, suggesting it belongs to a different universality class. We evaluate the exponent governing the bond fluctuations and our results agree with the Harris–Barghathi–Vojta criterium for relevant fluctuations.

Optimal reinforcement learning near the edge of a synchronization transition.

Recent experimental and theoretical studies have indicated that the putative criticality of cortical dynamics may correspond to a synchronization phase transition. The critical dynamics near such a critical point needs further investigation specifically when compared to the critical behavior near the standard absorbing state phase transition. Since the phenomena of learning and self-organized criticality (SOC) at the edge of synchronization transition can emerge jointly in spiking neural networks due to the presence of spike-timing dependent plasticity (STDP), it is tempting to ask the following: what is the relationship between synchronization and learning in neural networks? Further, does learning benefit from SOC at the edge of synchronization transition? In this paper, we intend to address these important issues. Accordingly, we construct a biologically inspired model of a cognitive system which learns to perform stimulus-response tasks. We train this system using a reinforcement learning rule implemented through dopamine-modulated STDP. We find that the system exhibits a continuous transition from synchronous to asynchronous neural oscillations upon increasing the average axonal time delay. We characterize the learning performance of the system and observe that it is optimized near the synchronization transition. We also study neuronal avalanches in the system and provide evidence that optimized learning is achieved in a slightly supercritical state.

Subdiffusive Activity Spreading in the Diffusive Epidemic Process.

The diffusive epidemic process is a paradigmatic example of an absorbing state phase transition in which healthy and infected individuals spread with different diffusion constants. Using stochastic activity spreading simulations in combination with finite-size scaling analyses we reveal two qualitatively different processes that characterize the critical dynamics: subdiffusive propagation of infection clusters and diffusive fluctuations in the healthy population. This suggests the presence of a strong-coupling regime and sheds new light on a long-standing debate about the theoretical classification of the system.

Absorbing-state phase transition and activated random walks with unbounded capacities

In this article, we study the existence of an absorbing-state phase transition of an Abelian process that generalises the Activated Random Walk (ARW). Given a vertex transitive $G=(V,E)$, we associate to each site $x \in V$ a capacity $w_x \ge 0$, which describes how many inactive particles $x$ can hold, where $\{w_x\}_{x \in V}$ is a collection of i.i.d random variables. When $G$ is an amenable graph, we prove that if $\mathbb E[w_x] 0$. Moreover, in the former case, we provide bounds for the critical density that match the ones available in the classical Activated Random Walk.

Balanced-imbalanced transitions in indirect reciprocity dynamics on networks.

Here we investigate the dynamics of indirect reciprocity on networks, a type of social dynamics in which the attitude of individuals, either cooperative or antagonistic, toward other individuals changes over time based upon their actions and mutual monitoring. We observe an absorbing state phase transition as we change the network's link or edge density. When the edge density is either small or large enough, opinions quickly reach an absorbing state, from which opinions never change anymore once reached. In contrast, if the edge density is in the middle range, the absorbing state is not reached and the state keeps changing, thus being active. The result shows an effect of social networks on spontaneous group formation.

Abelian oil and water dynamics does not have an absorbing-state phase transition

The oil and water model is an interacting particle system with two types of particles and a dynamics that conserves the number of particles, which belongs to the so-called class of Abelian networks. Widely studied processes in this class are sandpiles models and activated random walks, which are known (at least for some choice of the underlying graph) to undergo an absorbing-state phase transition. This phase transition characterizes the existence of two regimes, depending on the particle density: a regime of fixation at low densities, where the dynamics converges towards an absorbing state and each particle jumps only finitely many times, and a regime of activity at large densities, where particles jump infinitely often and activity is sustained indefinitely. In this work we show that the oil and water model is substantially different than sandpiles models and activated random walks, in the sense that it does not undergo an absorbing-state phase transition and is in the regime of fixation at all densities. Our result works in great generality: for any graph that is vertex transitive and for a large class of initial configurations.

Constraint relaxation leads to jamming.

Adding transitions to an equilibrium system increases the activity. Naively, one would expect this to hold also in out-of-equilibrium systems. We demonstrate, using relatively simple models, how adding transitions to an out of equilibrium system may in fact reduce the activity and even cause it to vanish. This surprising effect is caused by adding heretofore forbidden transitions into less and less active states. We investigate six related kinetically constrained lattice gas models, some of which behave as naively expected while others exhibit this nonintuitive behavior. These models exhibit an absorbing state phase transition, which is also affected by the added transitions. We introduce a semi-mean-field approximation describing the models, which agrees qualitatively with our numerical simulation.

Non-universal critical initial slip of parity conserving branching and annihilating random walkers with long-range diffusion

We consider a parity conserving model of branching and annihilating random walkers with long-range diffusion. We follow the short-time dynamics at the critical region to obtain the set of critical exponents associated to the growth in the number particles and its fluctuations, as well as the critical second-order moment ratio. Diffusion and branching processes are controlled by a diffusion probability p and the flight distance follows a Lévy distribution with exponent α. Three short-time scaling regimes are identified as a function of the Lévy exponent. For α≤5∕2 infinitesimal branching is relevant and leads to a finite density of walkers. An absorbing-state dynamic phase transition takes place at a finite branching probability for α>5∕2. Short-range power-law scaling occurs for α≥7∕2. In the intermediate regime, continuously varying exponents are obtained with the second-order cumulant depicting a non-monotonous behavior. The relative influence of Lévy diffusion and branching on the critical diffusion probability is also discussed.

Spike-Timing-Dependent Plasticity With Axonal Delay Tunes Networks of Izhikevich Neurons to the Edge of Synchronization Transition With Scale-Free Avalanches.

Critical brain hypothesis has been intensively studied both in experimental and theoretical neuroscience over the past two decades. However, some important questions still remain: (i) What is the critical point the brain operates at? (ii) What is the regulatory mechanism that brings about and maintains such a critical state? (iii) The critical state is characterized by scale-invariant behavior which is seemingly at odds with definitive brain oscillations? In this work we consider a biologically motivated model of Izhikevich neuronal network with chemical synapses interacting via spike-timing-dependent plasticity (STDP) as well as axonal time delay. Under generic and physiologically relevant conditions we show that the system is organized and maintained around a synchronization transition point as opposed to an activity transition point associated with an absorbing state phase transition. However, such a state exhibits experimentally relevant signs of critical dynamics including scale-free avalanches with finite-size scaling as well as critical branching ratios. While the system displays stochastic oscillations with highly correlated fluctuations, it also displays dominant frequency modes seen as sharp peaks in the power spectrum. The role of STDP as well as time delay is crucial in achieving and maintaining such critical dynamics, while the role of inhibition is not as crucial. In this way we provide possible answers to all three questions posed above. We also show that one can achieve supercritical or subcritical dynamics if one changes the average time delay associated with axonal conduction.

Critical Behavior of the Quantum Contact Process in One Dimension.

The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a nonequilibrium phase transition into an absorbing state that has been widely investigated and shown to belong to the directed percolation universality class. When the same process is considered in a quantum setting, much less is known. So far, mainly semiclassical studies have been conducted and the nature of the transition in low dimensions is still a matter of debate. Also, from a numerical point of view, from which the system may look fairly simple-especially in one dimension-results are lacking. In particular, the presence of the absorbing state poses a substantial challenge, which appears to affect the reliability of algorithms targeting directly the steady state. Here we perform real-time numerical simulations of the open dynamics of the quantum contact process and shed light on the existence and on the nature of an absorbing state phase transition in one dimension. We find evidence for the transition being continuous and provide first estimates for the critical exponents. Beyond the conceptual interest, the simplicity of the quantum contact process makes it an ideal benchmark problem for scrutinizing numerical methods for open quantum nonequilibrium systems.

Critical properties of a vector-mediated epidemic process

We study the critical behavior of an epidemic propagation model with interacting static individuals and diffusive vectors. The model presents a non-equilibrium phase transition from an absorbing vacuum state to an epidemic state at a critical vector density which depends on the recovery rates of infected individuals and vectors. The simulation was performed in a linear chain of the proposed model and the finite time scale hypothesis was explored to estimate the vector critical density and dynamic critical exponents. Our results show that the absorbing-state phase transition belongs to the universality class of the symmetric diffusive epidemic process irrespective to the relative values of the recovery rates. On the other hand, the critical vector density shows a much stronger dependence on the recovery rate of vectors than on the corresponding recovery rate of individuals.

Symbiotic contact process: Phase transitions, hysteresis cycles, and bistability

We performed Monte Carlo simulations of the symbiotic contact process on different spatial dimensions ($d$). On the complete and random graphs (infinite dimension), we observe hysteresis cycles and bistable regions, what is consistent with the discontinuous absorbing-state phase transition predicted by mean-field theory. By contrast, on a regular square lattice, we find no signs of bistability or hysteretic behavior. This result suggests that the transition in two dimensions is rather continuous. Based on our numerical observations, we conjecture that the nature of the transition changes at the upper critical dimension ($d_c$), from continuous ($d<d_c$) to discontinuous ($d>d_c$).

Conserved Manna model on Barabasi–Albert scale-free network

In this paper, a conserved Manna model is constructed and studied on Barabasi–Albert scale-free network with degree exponent γ = 3. Numerically I show that the system undergoes an absorbing state phase transition when the particle density is varied. Such a phase transition is characterized by measuring several critical exponents associated with the critical behaviour of the model. It has been found that the critical exponents exhibit mean field values of directed percolation. At the critical point, the spreading exponents have also been estimated. They satisfy the usual scaling relations. The effect of various initial conditions has been investigated and the result found to be independent of initial conditions, contrary to the fact that critical behaviour of such model highly depends on initial conditions when studied on regular lattice. The study confirms that though the Manna model in the lower dimensions exhibits different critical behavior other than DP, in the scale-free network it exhibits similar mean field result of DP class.