The effect of quenched disorder in neutral theories

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.

20 pages, 5 figures, to appear in JSTAT

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• Biased-voter model: how persuasive a small group can be?
• Pair approximation for the q-voter models with quenched disorder on networks
• Switching from a continuous to discontinuous phase transition under the quenched disorder
• Emergent spatial patterns of coexistence in species-rich plant communities
• Coexistence in neutral theories: interplay of criticality and mild local preferences
• Persistent individual bias in a voter model with quenched disorder
• The advantage of being slow: the quasi-neutral contact process
• Random field disorder at an absorbing state transition in one and two dimensions
• Time to absorption for a heterogeneous neutral competition model
• Critical phenomena in presence of symmetric absorbing states: a microscopic spin model with tunable parameters
• Quenched disorder in the contact process on bipartite sublattices
• Voter-like dynamics with conflicting preferences on modular networks
• Reputation-Driven Voting Dynamics