Diffusion disorder in the contact process

TL;DR

This paper investigates how spatially inhomogeneous diffusion affects the phase transition in the contact process, revealing that diffusion disorder destabilizes the critical point and leads to an infinite-randomness universality class.

Contribution

It demonstrates through simulations and theory that diffusion disorder induces effective healing rate disorder, altering the universality class of the transition.

Findings

Diffusion disorder destabilizes the clean directed percolation critical point.

The transition belongs to the infinite-randomness universality class.

Diffusion disorder generates effective healing rate disorder under renormalization.

Abstract

We study the effects of spatially inhomogeneous diffusion on the non-equilibrium phase transition in the contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a spatially uniform diffusion term. Correspondingly, we find quenched randomness in the diffusion rates to be irrelevant by power counting in the field-theory of the contact process. However, large-scale Monte Carlo simulations demonstrate that such diffusion disorder destabilizes the clean directed percolation critical point. Instead, the transition belongs to the same infinite-randomness universality class as the contact process with disorder in the infection or healing rates. To explain these results, we develop an effective model with an infinite diffusion rate; it shows that diffusion disorder generates an effective disorder in the healing rates. The same mechanism also appears in the field-theoretic description: Whereas diffusion disorder is irrelevant by power-counting, it generates standard random-mass disorder under renormalization. We discuss the validity of this mechanism for other absorbing state transitions and non-equilibrium phase transitions in general.