Absorbing-state Phase Transitions Research Articles

Continuum contact process and influence of impurity on the critical behavior in absorbing-state phase transitions in two dimensions.

We study via Monte Carlo simulations the influence of quenched and mobile impurities in the contact process (CP) on two-dimensional lattice and continuum systems. In the lattice system, the effect of mobile impurity was studied for the density n_{i}=0.2 and two selected values of hopping probability for impurity particles, w=0.5 and 1. In the continuum system, the CP was defined by distributing spherical impurity particles of diameter σ_{i} and number density n_{i}=0.2 and active particles of diameter unity and number density 1-n_{i} on a square substrate with periodic boundaries. In each dynamic process, a particle is selected at random; the active particle either creates with a rate λ an offspring at a distance r (1≤r≤1.5) from the active particle or annihilates with a unit rate, and the impurity particle hops a distance r (0≤r≤1), both along randomly selected directions. We found that the lattice CP shows power-law behaviors with varying critical exponents depending on the values of w. For the continuum CP with quenched impurity, the critical behavior followed the activated scaling scenario, whereas with mobile impurity usual power-law behaviors were observed but the critical exponents varied depending on the values of σ_{i}.

Visibility graphs of critical and off-critical time series for absorbing state phase transitions

Visibility graphs of critical and off-critical time series for absorbing state phase transitions

Reaction-Limited Quantum Reaction-Diffusion Dynamics.

We consider the quantum nonequilibrium dynamics of systems where fermionic particles coherently hop on a one-dimensional lattice and are subject to dissipative processes analogous to those of classical reaction-diffusion models. Particles can either annihilate in pairs, A+A→0, or coagulate upon contact, A+A→A, and possibly also branch, A→A+A. In classical settings, the interplay between these processes and particle diffusion leads to critical dynamics as well as to absorbing-state phase transitions. Here, we analyze the impact of coherent hopping and of quantum superposition, focusing on the so-called reaction-limited regime. Here, spatial density fluctuations are quickly smoothed out due to fast hopping, which for classical systems is described by a mean-field approach. By exploiting the time-dependent generalized Gibbs ensemble method, we demonstrate that quantum coherence and destructive interference play a crucial role in these systems and are responsible for the emergence of locally protected dark states and collective behavior beyond mean field. This can manifest both at stationarity and during the relaxation dynamics. Our analytical results highlight fundamental differences between classical nonequilibrium dynamics and their quantum counterpart and show that quantum effects indeed change collective universal behavior.

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.

An overview of epidemic models with phase transitions to absorbing states running on top of complex networks

Dynamical systems running on the top of complex networks have been extensively investigated for decades. But this topic still remains among the most relevant issues in complex network theory due to its range of applicability. The contact process (CP) and the susceptible–infected–susceptible (SIS) model are used quite often to describe epidemic dynamics. Despite their simplicity, these models are robust to predict the kernel of real situations. In this work, we review concisely both processes that are well-known and very applied examples of models that exhibit absorbing-state phase transitions. In the epidemic scenario, individuals can be infected or susceptible. A phase transition between a disease-free (absorbing) state and an active stationary phase (where a fraction of the population is infected) are separated by an epidemic threshold. For the SIS model, the central issue is to determine this epidemic threshold on heterogeneous networks. For the CP model, the main interest is to relate critical exponents with statistical properties of the network.

Continuously variable spreading exponents in the absorbing Nagel–Schreckenberg model

I study the critical behavior of a traffic model with an absorbing state. The model is a variant of the Nagel–Schreckenberg (NS) model, in which drivers do not decelerate if their speed is smaller than their headway, the number of empty sites between them and the car ahead. This makes the free-flow state (i.e. all vehicles traveling at the maximum speed, vmax, and with all headways greater than vmax) absorbing; such states are possible for densities ρ smaller than a critical value . Drivers with nonzero velocity, and with headway equal to velocity, decelerate with probability p. This absorbing Nagel–Schreckenberg (ANS) model, introduced in Iannini and Dickman (2017 Phys. Rev. E 95 022106), exhibits a line of continuous absorbing-state phase transitions in the ρ-p plane. Here I study the propagation of activity from a localized seed, and find that the active cluster is compact, as is the active region at long times, starting from uniformly distributed activity. The critical exponents δ (governing the decay of the survival probability) and η (governing the growth of activity) vary continuously along the critical curve. The exponents satisfy a hyperscaling relation associated with compact growth.

Nonequilibrium effective field theory for absorbing state phase transitions in driven open quantum spin systems

Phase transitions to absorbing states are among the simplest examples of critical phenomena out of equilibrium. The characteristic feature of these models is the presence of a fluctuationless configuration which the dynamics cannot leave, which has proved a rather stringent requirement in experiments. Recently, a proposal to seek such transitions in highly tuneable systems of cold atomic gases offers to probe this physics and, at the same time, to investigate the robustness of these transitions to quantum coherent effects. Here we specifically focus on the interplay between classical and quantum fluctuations in a simple driven open quantum model which, in the classical limit, reproduces a contact process, which is known to undergo a continuous transition in the "directed percolation" universality class. We derive an effective long-wavelength field theory for the present class of open spin systems and show that, due to quantum fluctuations, the nature of the transition changes from second to first order, passing through a bicritical point which appears to belong instead to the "tricritical directed percolation" class.

Background field functional renormalization group for absorbing state phase transitions.

We present a functional renormalization group approach for the active to inactive phase transition in directed percolation-type systems, in which the transition is approached from the active, finite density phase. By expanding the effective potential for the density field around its minimum, we obtain a background field action functional, which serves as a starting point for the functional renormalization group approach. Due to the presence of the background field, the corresponding nonperturbative flow equations yield remarkably good estimates for the critical exponents of the directed percolation universality class, even in low dimensions.

Continuous and discontinuous absorbing-state phase transitions on Voronoi-Delaunay random lattices.

We study absorbing-state phase transitions (APTs) in two-dimensional Voronoi-Delaunay (VD) random lattices with quenched coordination disorder. Quenched randomness usually changes the criticality and destroys discontinuous transitions in low-dimensional nonequilibrium systems. We performed extensive simulations of the Ziff-Gulari-Barshad model, and verified that the VD disorder does not change the nature of its discontinuous transition. Our results corroborate recent findings of Barghathi and Vojta [H. Barghathi and T. Vojta, Phys. Rev. Lett. 113, 120602 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.120602], stating the irrelevance of topological disorder in a class of random lattices that includes VD, and raise the interesting possibility that disorder in nonequilibrium APT may, under certain conditions, be irrelevant for the phase coexistence. We also verify that the VD disorder is irrelevant for the critical behavior of models belonging to the directed percolation and Manna universality classes.

Lifespan method as a tool to study criticality in absorbing-state phase transitions.

In a recent work, a new numerical method (the lifespan method) has been introduced to study the critical properties of epidemic processes on complex networks [M. Boguñá, C. Castellano, and R. Pastor-Satorras, Phys. Rev. Lett. 111, 068701 (2013)]. Here, we present a detailed analysis of the viability of this method for the study of the critical properties of generic absorbing-state phase transitions in lattices. Focusing on the well-understood case of the contact process, we develop a finite-size scaling theory to measure the critical point and its associated critical exponents. We show the validity of the method by studying numerically the contact process on a one-dimensional lattice and comparing the findings of the lifespan method with the standard quasistationary method. We find that the lifespan method gives results that are perfectly compatible with those of quasistationary simulations and with analytical results. Our observations confirm that the lifespan method is a fully legitimate tool for the study of the critical properties of absorbing phase transitions in regular lattices.

Mapping multiplicative to additive noise

The Langevin formulation of a number of well-known stochastic processes involves multiplicative noise. In this work we present a systematic mapping of a process with multiplicative noise to a related process with additive noise, which may often be easier to analyse. The mapping is easily understood in the example of the branching process. In a second example we study the random neighbour (or infinite range) contact process which is mapped to an Ornstein–Uhlenbeck process with absorbing wall. The present work might shed some light on absorbing state phase transitions in general, such as the role of conditional expectation values and finite size scaling, and elucidate the meaning of the noise amplitude. While we focus on the physical interpretation of the mapping, we also provide a mathematical derivation.

Experimental approaches to universal out-of-equilibrium scaling laws: turbulent liquid crystal and other developments

This is a brief survey of recent experimental studies on out-of-equilibrium scaling laws, focusing on two prominent situations where nontrivial universality classes have been identified theoretically: absorbing-state phase transitions and growing interfaces. First the paper summarizes the main results obtained for electrically driven turbulent liquid crystals, which exhibited the scaling laws for the directed percolation class at the transition between two turbulent regimes, and those for the Kardar–Parisi–Zhang class in the supercritical phase where one turbulent regime invades the other. Other experimental investigations on these universality classes and related situations are then overviewed and discussed. Some remarks on analyses of these scaling laws are also given from the practical viewpoint.

Phase transitions with infinitely many absorbing states in complex networks

We investigate the properties of the threshold contact process (TCP), a process showing an absorbing-state phase transition with infinitely many absorbing states, on random complex networks. The finite-size scaling exponents characterizing the transition are obtained in a heterogeneous mean-field (HMF) approximation and compared with extensive simulations, particularly in the case of heterogeneous scale-free networks. We observe that the TCP exhibits the same critical properties as the contact process, which undergoes an absorbing-state phase transition to a single absorbing state. The accordance among the critical exponents of different models and networks leads to conjecture that the critical behavior of the contact process in a HMF theory is a universal feature of absorbing-state phase transitions in complex networks, depending only on the locality of the interactions and independent of the number of absorbing states. The conditions for the applicability of the conjecture are discussed considering a parallel with the susceptible-infected-susceptible epidemic spreading model, which in fact belongs to a different universality class in complex networks.

Active-to-absorbing-state phase transition in the presence of fluctuating environments: Weak and strong dynamic scaling

We investigate the scaling properties of phase transitions between survival and extinction (active-to-absorbing-state phase transition, AAPT) in a model that by itself belongs to the directed percolation (DP) universality class, interacting with a spatiotemporally fluctuating environment having its own nontrivial dynamics. We model the environment by (i) a randomly stirred fluid, governed by the Navier-Stokes (NS) equation, and (ii) a fluctuating surface, described either by the Kardar-Parisi-Zhang (KPZ) or the Edward-Wilkinson (EW) equations. We show, by using a one-loop perturbative field theoretic setup that, depending upon the spatial scaling of the variance of the external forces that drive the environment (i.e., the NS, KPZ, or EW equations), the system may show weak or strong dynamic scaling at the critical point of active-to-absorbing-state phase transitions. In the former case AAPT displays scaling belonging to the DP universality class, whereas in the latter case the universal behavior is different.

Connecting the microdynamics to the emergent macrovariables: Self-organized criticality and absorbing phase transitions in the deterministic lattice gas

We reinvestigate the Deterministic Lattice Gas introduced as a paradigmatic model of the 1/f spectra [Phys. Rev. Lett. 64, 3103 (1990)] arising according to the self-organized criticality scenario. We demonstrate that the density fluctuations exhibit an unexpected dependence on systems size and relate the finding to effective Langevin equations. The low-density behavior is controlled by the critical properties of the gas at the absorbing state phase transition. We also show that the deterministic lattice gas is in the Manna universality class of absorbing state phase transitions. This is in contrast to expectations in the literature that suggested that the entirely deterministic nature of the dynamics would put the model in a different universality class. To our knowledge this is the first fully deterministic member of the Manna universality class.

Absorbing-state phase transitions on percolating lattices

We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical percolation theory with the properties of the supercritical nonequilibrium system on a finite-size cluster. In the case of the contact process, the interplay between geometric criticality due to percolation and dynamical fluctuations of the nonequilibrium system leads to a different universality class. The critical point is characterized by ultraslow activated dynamical scaling and accompanied by strong Griffiths singularities. To confirm the universality of this exotic scaling scenario we also study the generalized contact process with several (symmetric) absorbing states and we support our theory by extensive Monte Carlo simulations.

Weakly disordered absorbing-state phase transitions

The effects of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class are revisited. Using a strong-disorder energy-space renormalization-group method, it is shown that for any amount of disorder the critical behavior is controlled by an infinite-randomness fixed point in the same universality class of the random transverse-field Ising models.

Absorbing-state phase transitions: Exact solutions of small systems

I derive precise results for absorbing-state phase transitions using exact (numerically determined) quasistationary (QS) probability distributions for small systems. Analysis of the contact process on rings of 23 or fewer sites yields critical properties (control parameter, order-parameter ratios, and critical exponents z and betanu_(perpendicular)) with an accuracy of 0.06% or better; precise results are also obtained for the pair contact process. The QS distribution yields insights on the statistical entropy of these models. Preliminary application to a model in the stochastic sandpile class is also described.

Equivalence of conditional and external field ensembles in absorbing-state phase transitions

I comment on the relation between two sampling methods for absorbing-state models. It is shown that a certain ensemble without external field conditional to activity coincides with the unconditional ensemble for sufficiently small external field. The actual physical processes involved are identical and the derivation of the identity of the scaling behavior relies on a single (established) scaling law. While the conditional ensemble by construction does not contain information about the system with large external field, it contains all the information about the limit of vanishing external field and about the vicinity of the critical point: finite size scaling as well as critical scaling in the temperature-like variable or in (small) external field.

How to discriminate easily between directed-percolation and Manna scaling

Here we compare critical properties of systems in the directed-percolation (DP) universality class with those of absorbing-state phase transitions occurring in the presence of a non-diffusive conserved field, i.e., transitions in the so-called Manna or C-DP class. Even if it is clearly established that these constitute two different universality classes, most of their universal features (exponents, moment ratios, scaling functions,...) are very similar, making it difficult to discriminate numerically between them. Nevertheless, as illustrated here, the two classes behave in a rather different way upon introducing a physical boundary or wall. Taking advantage of this, we propose a simple and fast method to discriminate between these two universality classes. This is particularly helpful in solving some existing discrepancies in self-organized critical systems as sandpiles.