The contact process in heterogeneous and weakly-disordered systems

TL;DR

This paper investigates the critical behavior of the contact process in heterogeneous and weakly-disordered systems using series expansion and Monte Carlo simulations, confirming universality class retention or change.

Contribution

It provides a general analytical expression for critical points in weak-disorder limits and compares critical exponents in different environments.

Findings

CP in heterogeneous environments remains in DP universality class

Disordered environments show continuously changing critical exponents

Phase-separation lines and critical exponents are calculated

Abstract

The critical behavior of the contact process (CP) in heterogeneous periodic and weakly-disordered environments is investigated using the supercritical series expansion and Monte Carlo (MC) simulations. Phase-separation lines and critical exponents $\beta$ (from series expansion) and $\eta$ (from MC simulations) are calculated. A general analytical expression for the locus of critical points is suggested for the weak-disorder limit and confirmed by the series expansion analysis and the MC simulations. Our results for the critical exponents show that the CP in heterogeneous environments remains in the directed percolation (DP) universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents.