Critical dynamics of the directed percolation with L\'evy-driven temporally quenched disorder

TL;DR

This paper introduces a new model of directed percolation with Le9vy-driven temporally quenched disorder, revealing how disorder influences critical behavior and phase transition dynamics.

Contribution

It develops a novel temporally quenched disorder method using Le9vy distribution in a (1+1)-D DP model and analyzes its impact on critical exponents and phase transition.

Findings

Critical region varies with Le9vy parameter b.

Significant changes in decay and spreading exponents with b.

Disorder influences phase transition properties.

Abstract

Quenched disorder in absorbing phase transitions can disrupt the structure and symmetry of reaction-diffusion processes, offering a more accurate mapping to real physical systems. We developed a temporally quenched disorder method in the (1+1)-dimensional direct percolation (DP) model, where the increment of conditional probability is determined by the cumulative distribution function (CDF) of the L\'evy distribution. Monte Carlo (MC) simulations reveal that the model has a critical region governing the transition between absorbing and active states, and this region changes as the parameter $\beta$, which influences distribution properties. Guided by dynamic scaling laws, we observe that significant variations in the L\'evy distribution parameter $\beta$ lead to notable changes in the particle density decay exponent $\alpha$, total particle number exponent $\theta$, and spreading exponent $\tilde{z}$. The quenching mechanism we introduced has broad potential applications in various theoretical and experimental studies of absorbing phase transitions.