Generic two-phase coexistence, relaxation kinetics, and interface propagation in the quadratic contact process: simulation studies

Quenched disorder forbids discontinuous transitions in nonequilibrium low-dimensional systems

Quenched disorder affects significantly the behavior of phase transitions. The Imry-Ma-Aizenman-Wehr-Berker argument prohibits first-order or discontinuous transitions and their concomitant phase coexistence in low-dimensional equilibrium systems in the presence of random fields. Instead, discontinuous transitions become rounded or even continuous once disorder is introduced. Here we show that phase coexistence and first-order phase transitions are also precluded in nonequilibrium low-dimensional systems with quenched disorder: discontinuous transitions in two-dimensional systems with absorbing states become continuous in the presence of quenched disorder. We also study the universal features of this disorder-induced criticality and find them to be compatible with the universality class of the directed percolation with quenched disorder. Thus, we conclude that first-order transitions do not exist in low-dimensional disordered systems, not even in genuinely nonequilibrium systems with absorbing states.

Phase transitions in the quadratic contact process on complex networks

The quadratic contact process (QCP) is a natural extension of the well-studied linear contact process where infected (1) individuals infect susceptible (0) neighbors at rate λ and infected individuals recover (1→0) at rate 1. In the QCP, a combination of two 1's is required to effect a 0→1 change. We extend the study of the QCP, which so far has been limited to lattices, to complex networks. We define two versions of the QCP: vertex-centered (VQCP) and edge-centered (EQCP) with birth events 1-0-1→1-1-1 and 1-1-0→1-1-1, respectively, where "-" represents an edge. We investigate the effects of network topology by considering the QCP on random regular, Erdős-Rényi, and power-law random graphs. We perform mean-field calculations as well as simulations to find the steady-state fraction of occupied vertices as a function of the birth rate. We find that on the random regular and Erdős-Rényi graphs, there is a discontinuous phase transition with a region of bistability, whereas on the heavy-tailed power-law graph, the transition is continuous. The critical birth rate is found to be positive in the former but zero in the latter.

Metastability in Schloegl's second model for autocatalysis: Lattice-gas realization with particle diffusion

We analyze metastability associated with a discontinuous nonequilibrium phase transition in a stochastic lattice-gas realization of Schloegl's second model for autocatalysis. This model realization involves spontaneous annihilation, autocatalytic creation, and diffusion of particles on a square lattice, where creation at empty sites requires an adjacent diagonal pair of particles. This model, also known as the quadratic contact process, exhibits discontinuous transition between a populated active state and a particle-free vacuum or "poisoned" state, as well as generic two-phase coexistence. The poisoned state exists for all particle annihilation rates p>0 and hop rates h≥0 and is an absorbing state in the sense of Markovian processes. The active or reactive steady state exists only for p below a critical value, p{e}=p{e}(h) , but a metastable extension appears for a range of higher p up to an effective upper spinodal point, p{s+}=p{s+}(h) (i.e., p{s+}>p{e} ). For selected h , we assess the location of p{s+}(h) by characterizing both the poisoning kinetics and the propagation of interfaces separating vacuum and active states as a function of p .

Sustainability of dioecious and hermaphrodite populations on a lattice

Sexual reproduction may be divided into two main categories: hermaphroditism and dioecy (Botany)/gonochorism (Zoology). Simultaneous hermaphrodites can function in both male and female roles whereas a dioecious/gonochorist population consists of distinct male and female individuals. Mean-field calculations, which ignore spatial aspects, suggest that self-incompatible hermaphrodites should have a twofold advantage over dioecious population when reproduction is limited by mating encounters. By use of stochastic spatial simulations we demonstrate that hermaphroditism has an even greater advantage when local interactions are considered. This result provides further support for the observation that hermaphroditism is associated with sedentary species, such as plants and animals with poor mate search efficiency. We also investigate the finite size effects associated with the well-known quadratic contact process.

Schloegl's second model for autocatalysis with particle diffusion: Lattice-gas realization exhibiting generic two-phase coexistence

We analyze a discontinuous nonequilibrium phase transition between an active (or reactive) state and a poisoned (or extinguished) state occurring in a stochastic lattice-gas realization of Schloegl's second model for autocatalysis. This realization, also known as the quadratic contact process, involves spontaneous annihilation, autocatalytic creation, and diffusion of particles on a square lattice, where creation at empty sites requires a suitable nearby pair of particles. The poisoned state exists for all annihilation rates p>0 and is an absorbing particle-free "vacuum" state. The populated active steady state exists only for p below a critical value, p(e). If p(f) denotes the critical value below which a finite population can survive, then we show that p(f)<p(e). This strict inequality contrasts a postulate of Durrett, and is a direct consequence of the occurrence of coexisting stable active and poisoned states for a finite range p(f)<or=p<or=p(e) (which shrinks with increasing diffusivity). This so-called generic two-phase coexistence markedly contrasts behavior in thermodynamic systems. However, one still finds metastability and nucleation phenomena similar to those in discontinuous equilibrium transitions.