Crossover from directed percolation to mean field behavior in the diffusive contact process

TL;DR

This paper investigates how the diffusive contact process transitions from directed percolation to mean field behavior as diffusion increases, extending previous one-dimensional results to higher dimensions through theoretical and numerical methods.

Contribution

It refines and extends the understanding of the crossover exponent in the diffusive contact process to four spatial dimensions using field theory and simulations.

Findings

Crossover exponent bounds are refined up to four dimensions.

The transition from directed percolation to mean field behavior is characterized.

Numerical simulations support the theoretical predictions.

Abstract

Recently Dantas, Oliveira and Stilck [J. Stat. Mech. (2007) P08009] studied how the one-dimensional diffusive contact process crosses over from the critical behavior of directed percolation to an effective mean field behaviour when the diffusion rate is sent to infinity. They showed that this crossover can be described in terms of a crossover exponent $\phi$, finding the boundaries 3 <= $\phi$ <= 4 in one spatial dimension. In the present work we refine and extend this result up to four spatial dimensions by a field-theoretic calculation and extensive numerical simulations.