Study of universality crossover in the contact process

TL;DR

This paper investigates the crossover between directed percolation and compact percolation universality classes in a generalized contact process model, providing precise estimates of the crossover exponent through series expansions.

Contribution

The study introduces a generalized contact process with an autocatalytic process and accurately estimates the crossover exponent between universality classes.

Findings

Crossover occurs between directed and compact percolation universality classes.

Crossover exponent estimated as approximately 2.

Series expansion techniques effectively analyze the crossover behavior.

Abstract

We consider a generalization of the contact process stochastic model, including an additional autocatalitic process. The phase diagram of this model in the proper two-parameter space displays a line of transitions between an active and an absorbing phase which starts at the critical point of the contact process and ends at the transition point of the voter model. Thus, a crossover between the directed percolation and the compact percolation universality classes is observed at this latter point. We study this crossover by a variety of techniques. Using supercritical series expansions analyzed with partial differential approximants, we obtain precise estimates of the crossover behavior of the model. In particular, we find an estimate for the crossover exponent $\phi=2.00 \pm 0.02$. We also show arguments that support the conjecture $\phi=2$.