Efficient simulation of the random-cluster model

Elçi, Eren Metin; Weigel, Martin

doi:10.1103/physreve.88.033303

Cited by 15 publications

(20 citation statements)

References 59 publications

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“…For the integer values Q = 1, 2, 3, and 4, our simulations were performed using the Swendsen-Wang algorithm [29]. For Q = 0.5, we used a recent implementation of Sweeny's single-bond method [30] based on a poly-logarithmic connectivity algorithm [31]. For TABLE II.…”

Section: Numerical Resultsmentioning

confidence: 99%

Corner contribution to cluster numbers in the Potts model

et al. 2014

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Original citation:Kovacs, Istvan A., Elci, Eren Metin., Weigel, Martin., and Igloi, Ferenc Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders. For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N of clusters that intersect a given contour . To leading order, N is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of . These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition, we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are not found to be consistent with the values obtained by analytic continuation, as conventionally assumed. CURVE is the Institutional Repository for Coventry University

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Section: Numerical Resultsmentioning

confidence: 99%

Corner contribution to cluster numbers in the Potts model

et al. 2014

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“…Doing so requires to scan a number of bonds proportional to the typical size of the clusters. Close to the phase transition the clusters grow with the volume according to some critical exponent β and the computational cost hence grows like O(L β ) [26]. In contrast, a nearly-optimal solution for the fully-dynamic connectivity problem makes use of a spanning forest of Euler tour trees [27,28] in order to maintain a data structure which allows for an efficient checking of the bridge property.…”

Section: B Fully-dynamic Connectivity Problemmentioning

confidence: 99%

Solution of the sign problem in the Potts model at fixed fermion number

et al. 2018

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We consider the heavy-dense limit of QCD at finite fermion density in the canonical formulation and approximate it by a three-state Potts model. In the strong-coupling limit, the model is free of the sign problem. Away from the strong coupling, the sign problem is solved by employing a cluster algorithm which allows to average each cluster over the Zð3Þ sectors. Improved estimators for physical quantities can be constructed by taking into account the triality of the clusters, that is, their transformation properties with respect to Zð3Þ transformations.

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“…There are a few efficient methods [25] to simulate the RC model. In the present paper, we combine the colorassignation [26,27] and the Swendsen-Wang [28] methods together to design a highly efficient cluster algorithm with a small critical slowing-down phenomenon.…”

Section: Algorithm and The Sampled Quantitiesmentioning

confidence: 99%

Percolation of the site random-cluster model by Monte Carlo method

2015

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We propose a site random cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the Swendsen-Wang methods to design a highly efficient cluster algorithm with a small critical slowing-down phenomenon. To verify whether or not it is consistent with the bond random cluster model, we measure several quantities such as the wrapping probability Re, the percolating cluster density P∞, and the magnetic susceptibility per site χp as well as two exponents such as the thermal exponent yt and the fractal dimension y h of the largest percolating cluster. We find that for different exponents of cluster weight q = 1.5, 2, 2.5, 3, 3.5 and 4, the numerical estimation of the exponents yt and y h are consistent with the theoretical values. The universalities of the site random cluster model and the bond random cluster model are completely identical. For larger values of q, we find obvious signatures of the first-order percolation transition by the histograms and the hysteresis loops of percolating cluster density and the energy per site. Our results are helpful for the understanding of the percolation of traditional statistical models.

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Efficient simulation of the random-cluster model

Cited by 15 publications

References 59 publications

Corner contribution to cluster numbers in the Potts model

Corner contribution to cluster numbers in the Potts model

Solution of the sign problem in the Potts model at fixed fermion number

Percolation of the site random-cluster model by Monte Carlo method

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