Dynamic connectivity algorithms for Monte Carlo simulations of the random-cluster model

Elçi, Eren Metin; Weigel, Martin

doi:10.1088/1742-6596/510/1/012013

Cited by 5 publications

(4 citation statements)

References 22 publications

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“…Meanwhile, it would be worth mentioning that there is no particular reason to use Swendsen-Wang algorithm for the Ising updates on the active subgraph in step 4. Actually, "any" valid Ising Monte Carlo method would suffice, such as worm algorithm [30], or Sweeny algorithm [31], or dynamic connectivity checking algorithm [32].…”

Section: Algorithm and Observablesmentioning

confidence: 99%

Phase transitions in 3D Ising model with cluster weight by Monte Carlo method

Wang,

Feng,

Zhang

et al. 2021

Preprint

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A cluster weight Ising model is proposed by introducing an additional cluster weight in the partition function of the traditional Ising model. It is equivalent to the O(n) loop model or ncomponent face cubic loop model on the two-dimensional lattice, but on the three-dimensional lattice, it is still not very clear whether or not these models have the same universality. In order to simulate the cluster weight Ising model and search for new universality class, we apply a cluster algorithm, by combining the color-assignation and the Swendsen-Wang methods. The dynamical exponent for the absolute magnetization is estimated to be z = 0.45(3) at n = 1.5, consistent with that by the traditional Swendsen-Wang methods. The numerical estimation of the thermal exponent yt and magnetic exponent ym, show that the universalities of the two models on the three dimensional lattice are different. We obtain the global phase diagram containing paramagnetic and ferromagnetic phases. The phase transition between the two phases are second order at 1 ≤ n < nc and first order at n ≥ nc, where nc ≈ 2. The scaling dimension yt equals to the system dimension d when the first order transition occurs. Our results are helpful in the understanding of some traditional statistical mechanics models.

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Section: Algorithm and Observablesmentioning

confidence: 99%

Phase transitions in 3D Ising model with cluster weight by Monte Carlo method

Wang,

Feng,

Zhang

et al. 2021

Preprint

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“…The fermion update in our algorithm for example only requires connectivity queries for which the Find-Union ansatz is most efficient. Finally we note that the efficiencies of some of the strategies discussed above have been investigated, and when possible compared to the one of the Swendsen-Wang algorithm, for the generic random cluster model in two dimensions in [26,30].…”

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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“…Sweeny [46] proposed an algorithm for performing the necessary connectivity checks, which was applicable to planar graphs. In [14,15,16], it was demonstrated that this algorithmic problem can be efficiently solved by utilizing, and adapting, dynamic connectivity algorithms and appropriate data structures introduced in [29]. These latter methods are applicable to arbitrary graphs, and can perform the required pivotality tests in time which is poly-logarithmic in the graph size.…”

Section: )mentioning

confidence: 99%

“…In this article, we present a detailed study of the coupling time for the heat-bath dynamics of the Fortuin-Kasteleyn (FK) random-cluster model. This process is one of the examples originally considered in [43], and has been the subject of several recent studies [44,26,15,16,10]. As discussed in more detail below, when the cluster fugacity q ≥ 1, this process possesses an important monotonicity property, which makes it an ideal candidate for an efficient implementation of CFTP.…”

Section: Introductionmentioning

confidence: 99%

On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model

et al. 2017

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We consider the coupling from the past implementation of the randomcluster heat-bath process, and study its random running time, or coupling time. We focus on hypercubic lattices embedded on tori, in dimensions one to three, with cluster fugacity at least one. We make a number of conjectures regarding the asymptotic behaviour of the coupling time, motivated by rigorous results in one dimension and Monte Carlo simulations in dimensions two and three. Amongst our findings, we observe that, for generic parameter values, the distribution of the appropriately standardized coupling time converges to a Gumbel distribution, and that the standard deviation of the coupling time is asymptotic to an explicit universal constant multiple of the relaxation time. Perhaps surprisingly, we observe these results to hold both off criticality, where the coupling time closely mimics the coupon collector's problem, and also at the critical point, provided the cluster fugacity is below the value at which the transition becomes discontinuous. Finally, we consider analogous questions for the single-spin Ising heat-bath process.

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Dynamic connectivity algorithms for Monte Carlo simulations of the random-cluster model

Cited by 5 publications

References 22 publications

Phase transitions in 3D Ising model with cluster weight by Monte Carlo method

Phase transitions in 3D Ising model with cluster weight by Monte Carlo method

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

On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model

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