Phase transition in conservative diffusive contact processes

TL;DR

This study uses numerical simulations to explore phase transitions in conservative diffusive contact processes, revealing how the nature of the transition changes with diffusion rate and particle creation mechanisms.

Contribution

It provides the first detailed phase diagrams for these models, showing the transition from continuous to first-order with increasing diffusion rate.

Findings

Single-creation model remains continuous at all diffusion rates.

Pair- and triplet-creation models exhibit first-order transitions at high diffusion.

As diffusion rate approaches infinity, density jumps are 2/3 and 5/6 for pair- and triplet-creation models.

Abstract

We determine the phase diagrams of conservative diffusive contact processes by means of numerical simulations. These models are versions of the ordinary diffusive single-creation, pair-creation and triplet-creation contact processes in which the particle number is conserved. The transition between the frozen and active states was determined by studying the system in the subcritical regime and the nature of the transition, whether continuous or first order, was determined by looking at the fractal dimension of the critical cluster. For the single-creation model the transition remains continuous for any diffusion rate. For pair- and triplet-creation models, however, the transition becomes first order for high enough diffusion rate. Our results indicate that in the limit of infinite diffusion rate the jump in density equals 2/3 for the pair-creation model and 5/6 for the triplet-creation model.