# Effects of diffusion in competitive contact processes on bipartite lattices

## TL;DR

This study explores how particle diffusion affects phase transitions and sublattice ordering in a two-dimensional competitive contact process, revealing that low diffusion preserves ordering while high diffusion suppresses it, without changing critical behavior.

## Contribution

It introduces a detailed analysis of diffusion effects on bipartite contact processes, identifying thresholds for phase stability and confirming universality class robustness.

## Key findings

- Low diffusion maintains sublattice ordering.
- High diffusion suppresses sublattice ordering.
- Critical behavior remains unchanged by diffusion.

## Abstract

We investigate the influence of particle diffusion in the two-dimension contact process (CP) with a competitive dynamics in bipartite sublattices, proposed in [Phys. Rev. E 84, 011125 (2011)]. The particle creation depends on its first and second neighbors and the extinction increases according to the local density. In contrast to the standard CP model, mean-field theory and numerical simulations predict three stable phases: inactive (absorbing), active symmetric and active asymmetric, signed by distinct sublattice particle occupations. Our results from MFT and Monte Carlo simulations reveal that low diffusion rates do not destroy sublattice ordering, ensuring the maintenance of the asymmetric phase. On the other hand, for diffusion larger than a threshold value Dc, the sublattice ordering is suppressed and only the usual active (symmetric)-inactive transition is presented. We also show the critical behavior and universality classes are not affected by the diffusion.