Universality of the contact process with random dilution

TL;DR

This study uses quasi-stationary simulations to investigate the two-dimensional contact process with random site dilution, revealing that static critical exponents are unaffected by dilution, but critical moment ratios deviate from the universal value.

Contribution

It demonstrates the universality of static exponents in the contact process despite quenched disorder from random dilution.

Findings

Static exponents are independent of dilution fraction.

Critical moment ratios deviate from the universal value due to rare regions.

Disorder influences the statistics but not the critical exponents.

Abstract

We present quasi-stationary simulations of the two-dimensional contact process with quenched disorder included through the random dilution of a fraction of the lattice sites (these sites are not susceptible to infection). Our results strongly indicate that the static exponents are independent of the immunization fraction. In addition, the critical moment ratios $m=<\rho^2>/<\rho>^2$ deviate from the universal ratio $m=1.328$, observed for the non-dilluted system, to smaller values due to rare favorable regions which dominate the statistics.