Absorbing-state phase transitions on percolating lattices

TL;DR

This paper investigates how nonequilibrium phase transitions occur on percolating lattices, revealing a new universality class characterized by ultraslow scaling and Griffiths singularities, supported by theoretical analysis and Monte Carlo simulations.

Contribution

It develops a combined percolation and nonequilibrium theory to describe phase transitions on diluted lattices, identifying a novel universality class with unique scaling behavior.

Findings

Discovery of a new universality class with ultraslow activated scaling.

Identification of Griffiths singularities near the percolation threshold.

Validation of the theory through extensive Monte Carlo simulations.

Abstract

We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical percolation theory with the properties of the supercritical nonequilibrium system on a finite-size cluster. In the case of the contact process, the interplay between geometric criticality due to percolation and dynamical fluctuations of the nonequilibrium system leads to a new universality class. The critical point is characterized by ultraslow activated dynamical scaling and accompanied by strong Griffiths singularities. To confirm the universality of this exotic scaling scenario we also study the generalized contact process with several (symmetric) absorbing states, and we support our theory by extensive Monte-Carlo simulations.