The effect of quenched disorder in neutral theories

TL;DR

This paper investigates how quenched disorder influences phase transitions and symmetry breaking in neutral models like the voter model, revealing that disorder can induce phase transitions and affect symmetry breaking in low-dimensional systems.

Contribution

It demonstrates that quenched disorder prevents the separation of symmetry breaking and phase transitions in non-linear voter models, unifying these phenomena in low dimensions.

Findings

Disorder favors coexistence and induces phase transitions in the voter model.

In non-linear models, disorder couples symmetry breaking with phase transitions in low dimensions.

The Imry-Ma argument's limitations are highlighted in non-equilibrium transitions with disorder.

Abstract

We study systems with two symmetric absorbing states, such as the voter model and variations of it, which have been broadly used as minimal neutral models in genetics, population ecology, sociology, etc. We analyze the effects of a key ingredient ineluctably present in most real applications: random-field-like quenched disorder. In accord with simulations and previous findings, coexistence between the two competing states/opinions turns out to be strongly favored by disorder in the standard voter model; actually, a disorder-induced phase transition is generated for any finite system size in the presence of an arbitrary small spontaneous-inversion rate (preventing absorbing states from being stable). For non-linear versions of the voter model a general theory (by AlHammal et al.) explains that the spontaneous breaking of the up/down symmetry and an absorbing state phase transition can occur either together or separately, giving raise to two different scenarios. Here, we show that he presence of quenched disorder in non-linear voter models does not allow the separation of the up-down (Ising-like) symmetry breaking from the active-to-absorbing phase transition in low-dimensional systems: both phenomena can occur only simultaneously, as a consequence of the well-known Imry-Ma argument generalized to these non-equilibrium problems. When the two phenomena occur at unison, resulting into a genuinely non-equilibrium ("Generalized Voter") transition, the Imry-Ma argument is violated and the symmetry can be spontaneously broken even in low dimensions.