Critical behavior of the diffusive susceptible-infected-recovered model

TL;DR

This study investigates how diffusion affects the critical behavior of the susceptible-infected-recovered model on lattices, revealing that diffusion introduces distinct dynamical and stationary critical behaviors and causes crossover phenomena due to multiple scales.

Contribution

It demonstrates that diffusion acts as a singular perturbation, altering the critical behavior and causing crossover effects in the SIR model on lattices, which was not previously understood.

Findings

Diffusion destroys the duality symmetry of the non-diffusive model.

Diffusive SIR exhibits different critical behavior from the non-diffusive case.

Crossover behavior arises from interference of multiple length and time scales.

Abstract

The critical behavior of the non-diffusive susceptible-infected-recovered model on lattices had been well established in virtue of its duality symmetry. By performing simulations and scaling analyses for the diffusive variant on the two-dimensional lattice, we show that diffusion for all agents, while rendering this symmetry destroyed, constitutes a singular perturbation that induces asymptotically distinct dynamical and stationary critical behavior from the non-diffusive model. In particular, the manifested crossover behavior in the effective mean-square radius exponents reveals that slow crossover behavior in general diffusive multi-species reaction systems may be ascribed to the interference of multiple length scales and timescales at early times.