Contact process with sublattice symmetry breaking

TL;DR

This paper investigates a contact process with sublattice symmetry breaking, revealing multiple phases and phase transitions, including symmetric and asymmetric active states, with results supported by mean-field theory and Monte Carlo simulations.

Contribution

It introduces a contact process model with specific neighbor interactions and inhibition, predicting new phase behavior and confirming universality classes through simulations.

Findings

Three phases: inactive, active symmetric, active asymmetric

Phase transitions are continuous except when first-neighbor creation rate is zero

Transitions belong to Ising and directed percolation universality classes

Abstract

We study a contact process with creation at first- and second-neighbor sites and inhibition at first neighbors, in the form of an annihilation rate that increases with the number of occupied first neighbors. Mean-field theory predicts three phases: inactive (absorbing), active symmetric, and active asymmetric, the latter exhibiting distinct sublattice densities on a bipartite lattice. These phases are separated by continuous transitions; the phase diagram is reentrant. Monte Carlo simulations in two dimensions verify these predictions qualitatively, except for a first-neighbor creation rate of zero. (In the latter case one of the phase transitions is discontinuous.) Our numerical results confirm that the symmetric-asymmetric transition belongs to the Ising universality class, and that the active-absorbing transition belongs to the directed percolation class, as expected from symmetry considerations.