Quasi-stationary simulations of the contact process on quenched networks

TL;DR

This study uses high-accuracy quasi-stationary simulations to analyze the contact process on quenched networks, confirming that critical behavior and finite size scaling are consistent with annealed networks, supporting the validity of heterogeneous mean-field theory.

Contribution

It demonstrates that the critical behavior of the contact process on quenched networks matches that on annealed networks, validating heterogeneous mean-field theory in this context.

Findings

Critical behavior is unaffected by quenched topology.

Anomalous finite size scaling exponents are identical to annealed networks.

Topological correlations do not alter the critical behavior.

Abstract

We present high-accuracy quasi-stationary (QS) simulations of the contact process in quenched networks, built using the configuration model with both structural and natural cutoffs. The critical behavior is analyzed in the framework of the anomalous finite size scaling which was recently shown to hold for the contact process on annealed networks. It turns out that the quenched topology does not qualitatively change the critical behavior, leading only (as expected) to a shift of the transition point. The anomalous finite size scaling holds with exactly the same exponents of the annealed case, so that we can conclude that heterogeneous mean-field theory works for the contact process on quenched networks, at odds with previous claims. Interestingly, topological correlations induced by the presence of the natural cutoff do not alter the picture.