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arXiv:2603.04844

Diffusion disorder in the contact process

Valentin Anfray, Manisha Dhayal, Hong-Yan Shih, Thomas Vojta

Published Mar 5, 2026• 0 citations
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Abstract

We study the effects of spatially inhomogeneous diffusion on the non-equilibrium phase transition in the contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a spatially uniform diffusion term. Correspondingly, we find quenched randomness in the diffusion rates to be irrelevant by power counting in the field-theory of the contact process. However, large-scale Monte Carlo simulations demonstrate that such diffusion disorder destabilizes the clean directed percolation critical point. Instead, the transition belongs to the same infinite-randomness universality class as the contact process with disorder in the infection or healing rates. To explain these results, we develop an effective model with an infinite diffusion rate; it shows that diffusion disorder generates an effective disorder in the healing rates. The same mechanism also appears in the field-theoretic description: Whereas diffusion disorder is irrelevant by power-counting, it generates standard random-mass disorder under renormalization. We discuss the validity of this mechanism for other absorbing state transitions and non-equilibrium phase transitions in general.

DOI
10.48550/arxiv.2603.04844

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We study the effects of spatially inhomogeneous diffusion on the non-equilibrium phase transition in the contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a spatially uniform diffusion term. Correspondingly, we find quenched randomness in the diffusion rates to be irrelevant by power counting in the field-theory of the contact process. However, large-scale Monte Carlo simulations demonstrate that such diffusion disorder destabilizes the clean directed percolation critical point. Instead, the transition belongs to the same infinite-randomness universality class as the contact process with disorder in the infection or healing rates. To explain these results, we develop an effective model with an infinite diffusion rate; it shows that diffusion disorder generates an effective disorder in the healing rates. The same mechanism also appears in the field-theoretic description: Whereas diffusion disorder is irrelevant by power-counting, it generates standard random-mass disorder under renormalization. We discuss the validity of this mechanism for other absorbing state transitions and non-equilibrium phase transitions in general.
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The contact process is a simple infection spreading model showcasing an out-of-equilibrium phase transition between a macroscopically active and an inactive phase. Such absorbing state phase transitions are often sensitive to the presence of quenched disorder. Traditionally, a phase transition in the disordered contact process is either triggered by dilution or by locally varying the infection rate. However, when both factors play an important role, a multicritical point emerges that remains poorly understood. Here, we study the multicritical contact process by large-scale Monte Carlo simulations in two and three dimensions. The multicritical behavior is found to be universal and exhibits ultra-slow, activated dynamical scaling, with exponents consistent with those predicted by the strong disorder renormalization group method. This finding indicates that the multicritical contact process belongs to the same universality class as the multicritical quantum Ising model, in both two and three dimensions.
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