Simulational study for the crossover in the generalized contact process with diffusion

TL;DR

This study investigates the crossover behavior in a generalized contact process with diffusion, using numerical simulations to estimate the crossover exponent at higher diffusion rates where previous analytical methods failed.

Contribution

It extends previous work by estimating the crossover exponent for higher diffusion rates through numerical simulations, beyond the weak diffusion regime.

Findings

Crossover exponent estimated for higher diffusion rates.

Weak diffusion regime shows crossover exponent ~2.

Numerical approach effective where analytical methods fail.

Abstract

In a recent work, Dantas and Stilck studied a model that generalizes the contact process model with diffusion. Our approach, based on the supercritical expansion, showed that for a weak diffusion regime the crossover exponent between the directed percolation and compact directed percolation universality classes was $\phi\approx 2$. However this approach did not work for reduced diffusion rates higher than $D\approx 0.3$, where $0\leq D\leq 1$ and D=1 corresponds to an infinite diffusion rate. Thus, in the present work we estimate this crossover exponent for higher diffusion rates using a numerical simulation approach.