Scaling behavior of the disordered contact process

TL;DR

This study investigates the one-dimensional disordered contact process using Monte Carlo simulations, revealing activated scaling behavior and disorder-dependent critical exponents that approach strong-disorder predictions but do not fully reach them.

Contribution

It provides the first comprehensive numerical evidence that activated scaling describes the disordered contact process across various disorder strengths.

Findings

Activated scaling is confirmed for all disorder levels studied.

Critical exponents depend on disorder strength and approach strong-disorder limits.

No evidence of strong-disorder exponents even at high disorder levels.

Abstract

The one-dimensional contact process with weak to intermediate quenched disorder in its transmission rates is investigated via quasi-stationary Monte Carlo simulation. We address the contested questions of both the nature of dynamical scaling, conventional or activated, as well as of universality of critical exponents by employing a scaling analysis of the distribution of lifetimes and the quasi-stationary density of infection. We find activated scaling to be the appropriate description for all disorder strengths considered. Critical exponents are disorder dependent and approach the values expected for the limit of strong disorder as predicted by strong-disorder renormalization group analysis of the process. However, even for the strongest disorder under consideration no strong-disorder exponents are found.