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Diffusion disorder in the contact process

Valentin Anfray1,*, Manisha Dhayal2,†, Hong-Yan Shih1,3,‡, and Thomas Vojta2,§

  • *Contact author: valentin.anfray@gmail.com
  • †Contact author: mdw6f@mst.edu
  • ‡Contact author: hongyan@as.edu.tw
  • §Contact author: vojtat@mst.edu
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Phys. Rev. E 114, 034112 – Published 8 September, 2026

DOI: https://doi.org/10.1103/73g3-b38r

Abstract

We study the effects of spatially inhomogeneous diffusion on the nonequilibrium phase transition in the unidimensional 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 at higher dimensions and for other absorbing state transitions and nonequilibrium phase transitions in general.

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Outline

Information

Phys. Rev. E 114, 034112– Published 8 September, 2026
  • Received 23 March 2026
  • Revised 23 June 2026
  • Accepted 21 August 2026
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