Influence of competition in minimal systems with discontinuous absorbing phase transitions

TL;DR

This paper investigates how competition between restrictive and standard contact process dynamics affects the nature of discontinuous absorbing phase transitions, using mean-field theory and simulations to reveal contrasting predictions and results.

Contribution

It introduces the study of competitive dynamics in minimal systems with discontinuous transitions, highlighting the impact on phase coexistence and transition nature.

Findings

Mean-field theory predicts large competition rates needed for transition change.

Numerical simulations show small competition rates can suppress phase coexistence.

Limited competition alters the discontinuous transition behavior.

Abstract

Contact processes (CP's) with particle creation requiring a minimal neighborhood (restrictive or threshold CP's) present a novel sort of discontinuous absorbing transitions, that revealed itself robust under the inclusion of different ingredients, such as distinct lattice topologies, particle annihilations and diffusion. Here, we tackle on the influence of competition between restrictive and standard dynamics (that describes the usual CP and a continuous DP transition is presented). Systems have been studied via mean-field theory (MFT) and numerical simulations. Results show partial contrast between MFT and numerical results. While the former predicts that considerable competition rates are required to shift the phase transition, the latter reveals the change occurs for rather limited (small) fractions. Thus, unlike previous ingredients (such as diffusion and others), limited competitive rates suppress the phase coexistence.