Effects of lattice dilution on the non-equilibrium phase transition in the stochastic Susceptible-Infectious-Recovered model

TL;DR

This study examines how site dilution affects the non-equilibrium phase transition in the SIR model, revealing long crossover effects that diminish with increased recovery rate or agent mobility, aligning the system with expected universality class behavior.

Contribution

It demonstrates the impact of quenched disorder and mobility on the critical behavior and crossover phenomena in the SIR model on lattices.

Findings

Long crossover regions observed in quenched disorder systems.

Increased recovery rate reduces transient effects.

Agent mobility shortens crossover duration.

Abstract

We investigate how site dilution, as would be introduced by immunization, affects the properties of the active-to-absorbing non-equilibrium phase transition in the paradigmatic Susceptible-Infectious-Recovered (SIR) model on regular cubic lattices. According to the Harris criterion, the critical behavior of the SIR model, which is governed by the universal scaling exponents of the dynamic isotropic percolation (DyIP) universality class, should remain unaltered after introducing impurities. However, when the SIR reactions are simulated for immobile agents on two- and three-dimensional lattices subject to quenched disorder, we observe a wide crossover region characterized by varying effective exponents. Only after a sufficient increase of the lattice sizes does it becomes clear that the SIR system must transition from that crossover regime before the effective critical exponents asymptotically assume the expected DyIP values. We attribute the appearance of this exceedingly long crossover to a time lag in a complete recovery of small disconnected clusters of susceptible sites which are apt to be generated when the system is prepared with Poisson-distributed quenched disorder. Finally, we demonstrate that this transient region becomes drastically diminished when we significantly increase the value of the recovery rate or enable diffusive agent mobility through short-range hopping.