Critical phenomena in the presence of symmetric absorbing states: A microscopic spin model with tunable parameters

Azizi, Ahmadreza; Pleimling, Michel

doi:10.1103/physreve.102.022112

Cited by 3 publications

(1 citation statement)

References 36 publications

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“…Sometime ago, it was noticed that the voter critical point can split, and the breaking of the up-down symmetry and the collapse into an absorbing state would take place separately [35]. Such an effect was explained in terms of the Langevin description [36] and observed in some other systems [37][38][39][40].…”

Section: Heat-bath Dynamicsmentioning

confidence: 99%

Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs

Lipowski,

Ferreira,

Lipowska

2023

Entropy

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Using a single-site mean-field approximation (MFA) and Monte Carlo simulations, we examine Ising-like models on directed regular random graphs. The models are directed-network implementations of the Ising model, Ising model with absorbing states, and majority voter models. When these nonequilibrium models are driven by the heat-bath dynamics, their stationary characteristics, such as magnetization, are correctly reproduced by MFA as confirmed by Monte Carlo simulations. It turns out that MFA reproduces the same result as the generating functional analysis that is expected to provide the exact description of such models. We argue that on directed regular random graphs, the neighbors of a given vertex are typically uncorrelated, and that is why MFA for models with heat-bath dynamics provides their exact description. For models with Metropolis dynamics, certain additional correlations become relevant, and MFA, which neglects these correlations, is less accurate. Models with heat-bath dynamics undergo continuous phase transition, and at the critical point, the power-law time decay of the order parameter exhibits the behavior of the Ising mean-field universality class. Analogous phase transitions for models with Metropolis dynamics are discontinuous.

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