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Main Authors: Wang, Yanyang, Yang, Yuxiang, Li, Wei
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2507.01490
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author Wang, Yanyang
Yang, Yuxiang
Li, Wei
author_facet Wang, Yanyang
Yang, Yuxiang
Li, Wei
contents 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 Lévy 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 $β$, which influences distribution properties. Guided by dynamic scaling laws, we observe that significant variations in the Lévy distribution parameter $β$ lead to notable changes in the particle density decay exponent $α$, total particle number exponent $θ$, and spreading exponent $\tilde{z}$. The quenching mechanism we introduced has broad potential applications in various theoretical and experimental studies of absorbing phase transitions.
format Preprint
id arxiv_https___arxiv_org_abs_2507_01490
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Critical dynamics of the directed percolation with Lévy-driven temporally quenched disorder
Wang, Yanyang
Yang, Yuxiang
Li, Wei
Statistical Mechanics
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 Lévy 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 $β$, which influences distribution properties. Guided by dynamic scaling laws, we observe that significant variations in the Lévy distribution parameter $β$ lead to notable changes in the particle density decay exponent $α$, total particle number exponent $θ$, and spreading exponent $\tilde{z}$. The quenching mechanism we introduced has broad potential applications in various theoretical and experimental studies of absorbing phase transitions.
title Critical dynamics of the directed percolation with Lévy-driven temporally quenched disorder
topic Statistical Mechanics
url https://arxiv.org/abs/2507.01490