A supercritical series analysis for the generalized contact process with diffusion

TL;DR

This paper investigates how diffusion influences the crossover between universality classes in a generalized contact process model, using series expansions and mean-field approximations to analyze critical behavior.

Contribution

It introduces a supercritical series expansion method to study the effect of diffusion on the crossover between directed percolation classes.

Findings

Crossover exponent remains close to 2 at high diffusion rates.

Critical line behavior differs from mean-field predictions.

Diffusion does not lead to mean-field limit as diffusion rate increases.

Abstract

We study a model that generalizes the CP with diffusion. An additional transition is included in the model so that at a particular point of its phase diagram a crossover from the directed percolation to the compact directed percolation class will happen. We are particularly interested in the effect of diffusion on the properties of the crossover between the universality classes. To address this point, we develop a supercritical series expansion for the ultimate survival probability and analyse this series using d-log Pad\'e and partial differential approximants. We also obtain approximate solutions in the one- and two-site dynamical mean-field approximations. We find evidences that, at variance to what happens in mean-field approximations, the crossover exponent remains close to $\phi=2$ even for quite high diffusion rates, and therefore the critical line in the neighborhood of the multicritical point apparently does not reproduce the mean-field result (which leads to $\phi=0$) as the diffusion rate grows without bound.