Comparing the influence of distinct kinds of temporal disorder in a low dimensional absorbing transition model

TL;DR

This study investigates how different types of temporal disorder affect a low-dimensional absorbing transition model, revealing that disorder can suppress or enhance reentrant phase behavior and influence critical universality classes.

Contribution

It introduces and compares two types of temporal disorder in a triplet annihilation model, analyzing their distinct impacts on phase diagrams and critical behavior.

Findings

Disorder in creation-annihilation suppresses reentrant phases at low diffusion.

Disorder in diffusion rate enhances reentrant behavior and maintains DP universality.

Critical behavior varies with disorder type and diffusion rate, affecting universality class.

Abstract

Recently one has stated that temporal disorder constitutes a relevant perturbation in absorbing phase transitions for all dimensions. However, its effect for systems other than the standard contact process (CP), its competition with other ingredients (e.g. particle diffusion) and other kinds of disorder (besides the standard types) are unknown. In order to shed some light in the above mentioned points, we investigate a variant of the usual CP, namely triplet annihilation model (TAM), in which the competition between triplet annihilation and single particle diffusion leads to an unusual phase diagram behavior, with reentrant shape and endless activity for sufficient large diffusion rates. Two kinds of time-dependent disorder have been considered. In the former, it is introduced in the creation-annihilation parameters (as commonly considered in recent studies), whereas in the latter the diffusion rate $D$ (so far unexplored) is allowed to be time dependent. In all cases, the disorder follows an uniform distribution with fixed mean and width $\sigma$. Two values of $\sigma$ have been considered, in order to exemplify the regime of "weaker" and "stronger" temporal disorder strengths. Our results show that in the former approach, the disorder suppresses the reentrant phase diagram with a critical behavior deviating from the directed percolation universality class (DP) in the regime of low diffusion rates, while they strongly suggest that the DP class is recovered for larger hoping rates. An opposite scenario is found in the latter disorder approach, with a substantial increase of reentrant shape and the maximum diffusion, in which the reentrant shape also displays a critical behavior consistent to the DP universality class (in similarity with the pure model). Lastly, comparison with the diffusive disordered CP has been undertaken.