A two-variable series for the contact process with diffusion

TL;DR

This paper develops a mathematical approach to analyze the contact process with diffusion, identifying the critical line and crossover behavior between universality classes in one dimension.

Contribution

It introduces a partial differential approximants technique to determine the critical line and crossover exponent for the contact process with diffusion.

Findings

Critical line of the contact process with diffusion determined.

Crossover exponent estimated for transition between universality classes.

Method applicable to similar nonequilibrium phase transition models.

Abstract

In this work we use the technique of the partial differential approximants to determine, from a pertubative supercritical series expansion for the ulimate survival probability, the critical line of the contact process model in one dimension with diffusion and estimate the value of the crossover exponent that characterizes the change of the critical behavior from the 1d directed percolation universality class to the mean-field directed percolation universality class. This crossover occurs in the limit of infinite diffusion rate.