Supercritical series expansion for the contact process in heterogeneous and disordered environments

TL;DR

This paper develops a supercritical series expansion method to analyze the critical behavior of the contact process in heterogeneous and disordered environments, confirming universality class in periodic cases and variable exponents in disordered systems.

Contribution

It introduces a novel supercritical series expansion approach combined with analytical techniques to study critical points and exponents in heterogeneous and disordered lattices.

Findings

Critical exponents in heterogeneous systems match homogeneous case, confirming directed percolation universality.

Disordered systems exhibit continuously varying critical exponents.

Analytical methods effectively evaluate critical points and exponents in complex environments.

Abstract

The supercritical series expansion of the survival probability for the one-dimensional contact process in heterogeneous and disordered lattices is used for the evaluation of the loci of critical points and critical exponents $\beta$. The heterogeneity and disorder are modeled by considering binary regular and irregular lattices of nodes characterized by different recovery rates and identical transmission rates. Two analytical approaches based on Nested Pad\'e approximants and Partial Differential approximants were used in the case of expansions with respect to two variables (two recovery rates) for the evaluation of the critical values and critical exponents. The critical exponents in heterogeneous systems are very close to those for the homogeneous contact process thus confirming that the contact process in periodic heterogeneous environment belongs to the directed percolation universality class. The disordered systems, in contrast, seem to have continuously varying critical exponents.