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

TL;DR

This paper uses quasi-stationary simulations to analyze three-dimensional models in the directed percolation universality class, clarifying critical behavior and transient effects in the contact process, SIS, and CRP models.

Contribution

It introduces quasi-stationary simulation methods for 3D models and clarifies the transient nature of mean-field exponents in the CRP model.

Findings

Moment ratios for DP class in 3D established

Mean-field exponent in CRP is a transient effect

Critical behavior characterized for CP, SIS, and CRP models

Abstract

We present quasi-stationary simulations of three-dimensional models with a single absorbing configuration, namely the contact process (CP), the susceptible-infected-susceptible (SIS) model and the contact replication process (CRP). The moment ratios of the order parameters for the DP class in three dimensions were set up using the well established SIS and CP models. We also show that the mean-field exponent for d = 3 reported previously for the CRP (Ferreira 2005 Phys. Rev. E 71 017104) is a transient observed in the spreading analysis.