Contact process with mobile disorder

TL;DR

This paper investigates the phase transition in a one-dimensional contact process with mobile disorder, revealing altered critical behavior and exponents due to diffusing inactive sites, with implications for understanding non-quenched disorder effects.

Contribution

It introduces a model with mobile disorder affecting the contact process, showing how critical exponents and scaling behavior differ from traditional directed percolation.

Findings

Critical exponents delta and z differ from directed percolation.

Critical creation rate increases with vacancy density and diverges at a threshold.

Scaling behavior simplifies at high vacancy density v_c < 1.

Abstract

I study the absorbing-state phase transition in the one-dimensional contact process with mobile disorder. In this model the dilution sites, though permanently inactive, diffuse freely, exchanging positions with the other sites, which host a basic contact process. Even though the disorder variables are not quenched, the critical behavior is affected: the critical exponents delta and z, the ratio beta/nu_perp and the moment ratio m= <rho^2>/rho^2 take values different from those of directed percolation, and appear to vary with the vacancy diffusion rate. While the survival probability starting from a single active seed follows the usual scaling, P(t) ~ t^{-delta}, at the critical point, the mean number of active sites and mean-square spread grow more slowly than power laws. The critical creation rate increases with the vacancy density v and diverges at a value v_c < 1. The scaling behavior at this point appears to be simpler than for smaller vacancy densities.