Quasi-stationary simulations of the directed percolation universality class ind= 3 dimensions

Abstract

Abstract. We present quasi-stationary simulations of three-dimensional models with a single absorbing configuration, viz. the contact process (CP), the susceptibleinfected-susceptible (SIS) and the contact replication process (CRP). The moment ratios of the order parameters for DP class in three dimensions were set up using the well established SIS and CP models. We also show that the mean-field exponents in d = 3 reported previously for CRP [Ferreira SC 2005 Phys. Rev Quasi-stationary simulations of DP class in d = 3 2 IntroductionPhase transitions to a single absorbing configuration, a state in which the system can not scape from, are nowadays a topic in the frontier of Nonequilibrium Statistical Physics [1,2]. Concomitantly with the increasing interest on absorbing/active phase transitions in complex topologies [3,4,5,6,7], there are still a lot of open problems being intensively investigated on regular lattices such as the effects of quenched disorder [8,9,10], diffusion [11], as well the modeling of predator-prey systems [12], and clonal replication [13,14].Under the renormalization group point of view, it is expected [1,15,16] that the absorbing phase transitions in models with a positive one-component order parameter, short-range interactions and without additional symmetries or quenched disorder belong generally to the universality class of directed percolation (DP). This conjecture is known as Janssen-Grassberger criterion [1]. It is worthwhile to mention, the interest on this kind of phase transitions was raised by the recent experimental observation of the DP class in absorbing-state phase transitions [18,19]. On the other hand, while DP is considered the most robust universality class of the absorbing-state phase transitions, the precise numerical determination of the critical exponents of a specific model can be masked by factors like diffusion [11] and weak quenched disorder [10].The contact process (CP), the standard example of the DP universality class, is a toy model of epidemics [20]. ‡. More recently, a novel variation of the CP was introduced for the modeling of clonal (copies of themselves) replication, the contact replication process (CRP) [13,14]. Since neither additional symmetries nor long-range interactions were included, the CRP fulfils the requirements of the Janssen-Gassberger criterion. However, the first dynamic spreading analysis of CRP in d = 1 − 3 dimensions, reported in [13,14] intriguingly classified the model in the DP universality class in one and two, but not in three dimensions. Surprisingly, in d = 3 the reported spreading exponents were those predicted by the mean-field approach [14].In the present work we applied spreading analysis and the method of quasistationary simulations [22,23] in three-dimensional models that fulfill the JanssenGrassberger criterion. Particularly, we turned back to the CRP model and showed that the mean-field behaviour observed previously in d = 3 [14] is a transient associated to the closeness between critical creation and annihilation events. ...

Monte Carlo simulations of the clean and disordered contact process in three dimensions

“…These values fulfill hyperscaling because Θ + 2δ − 3/z = −0.0005 (22), in excellent agreement with the exact result Value This work Ref. [51] Ref. [47] Ref.…”

“…However, they are clearly not compatible with the values given in Refs. [47] and [51] (for δ, the difference is about ten times the given error, and for z it is about five times the given error). We believe, this discrepancy can be traced back to the location of the critical point.…”

Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks

“…Symbols: N inf is the number of infected vertices; NSI is number of susceptible vertices with at least one infected nearest-neighbor; Ne is the number of edges emanating from infected vertices; and u is random variable uniformly distributed in the interval (0, 1). [36,37] SIS-A (all ) [38,39] SIS-S (standard ) [4] Infected…”

Quasistationary simulations of the contact process on quenched networks

“…Universal and size-independent moment ratios were studied for absorbing phase transitions in lattice models [29][30][31]. The size independence of moment ratios in lattice systems results from the scaling invariance close to the critical point (see, e.g., Ref.…”