Cluster percolation in the two-dimensional Ising spin glass

Münster, L.; Weigel, Martin

doi:10.1103/physreve.107.054103

Cited by 5 publications

(2 citation statements)

References 65 publications

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“…It is apparent that the typical clusters in the overlap are smaller than those in the two replicas, and that the hard constraint leads to smaller clusters than the soft constraint. We note that in the spin-glass setup, the prescription for soft-constrained clusters leads to what is there known as Houdayer clusters [28], while the hard constraint corresponds to a geometric-cluster version of the Chayes-Machta-Redner construction [30,32].…”

Section: Model and Simulation Detailsmentioning

confidence: 97%

“…Several types of clusters in the overlap of two copies, including geometric clusters, have been considered as potential candidates for the construction of cluster updates [26,28,29]. It is found there that the spin-glass transition is connected to the onset of a density difference of the two largest clusters of a suitable type, while percolation of such clusters occurs already above the spin-glass transition point [26,30]. As we shall see below, the clusters considered for the Ising model in the present work are related to some of the cluster types discussed in the context of the spin-glass transition, cf.…”

Section: Introductionmentioning

confidence: 99%

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Geometric clusters in the overlap of the Ising model

Akritidis,

Fytas,

Weigel

2023

Phys. Rev. E

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We study the percolation properties of geometrical clusters defined in the overlap space of two statistically independent replicas of a square-lattice Ising model that are simulated at the same temperature. In particular, we consider two distinct types of clusters in the overlap, which we dub soft-and hard-constraint clusters, and which are subsets of the regions of constant spin overlap. By means of Monte Carlo simulations and a finite-size scaling analysis we estimate the transition temperature as well as the set of critical exponents characterizing the percolation transitions undergone by these two cluster types. The results suggest that both soft-and hardconstraint clusters percolate at the critical temperature of the Ising model and their critical behavior is governed by the correlation-length exponent ν = 1 found by Onsager. At the same time, they exhibit nonstandard and distinct sets of exponents for the average cluster size and percolation strength.

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Section: Model and Simulation Detailsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Geometric clusters in the overlap of the Ising model

Akritidis,

Fytas,

Weigel

2023

Phys. Rev. E

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In and beyond the Griffiths phase: A large-deviation study of the magnetic susceptibility of the two-dimensional bond-diluted Ising model

Münster,

Hartmann,

Weigel

2024

Phys. Rev. E

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Anomalous distribution of magnetization in an Ising spin glass with correlated disorder

Nishimori

2024

Phys. Rev. E

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The effect of correlations in disorder variables is a largely unexplored topic in spin glass theory. We study this problem through a specific example of correlated disorder introduced in the Ising spin glass model. We prove that the distribution function of the magnetization along the Nishimori line in the present model is identical to the distribution function of the spin glass order parameter in the standard Edwards-Anderson model with symmetrically distributed independent disorder. This result means that if the Edwards-Anderson model exhibits replica symmetry breaking, the magnetization distribution in the correlated model has support on a finite interval, in sharp contrast to the conventional understanding that the magnetization distribution has, at most, two delta peaks. This unusual behavior challenges the traditional argument against replica symmetry breaking on the Nishimori line in the Edwards-Anderson model. In addition, we show that when temperature chaos is present in the Edwards-Anderson model, the ferromagnetic phase is strictly confined to the Nishimori line in the present model. These findings are valid not only for finite-dimensional systems but also for the infinite-range model, and highlight the need for a deeper understanding of disorder correlations in spin glass systems. Published by the American Physical Society 2024

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Cluster percolation in the two-dimensional Ising spin glass

Cited by 5 publications

References 65 publications

Geometric clusters in the overlap of the Ising model

Geometric clusters in the overlap of the Ising model

In and beyond the Griffiths phase: A large-deviation study of the magnetic susceptibility of the two-dimensional bond-diluted Ising model

Anomalous distribution of magnetization in an Ising spin glass with correlated disorder

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