Loop-Cluster Coupling and Algorithm for Classical Statistical Models

Zhang, Lei; Michel, Manon; Elçi, Eren Metin; Deng, Youjin

doi:10.1103/physrevlett.125.200603

Cited by 9 publications

(9 citation statements)

References 48 publications

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“…(b), backtrack till the root site ( [2]), construct a flat tree (red arrows), and mark all the passing bonds as nonbridges (thick blue bonds). (c), apply the last-in-first-out rule so that the old elements [9], • • • , [6] are removed and and new elements, [6], [7], are added to the walk. (d), add a new loop and replace the existing root by the new one.…”

Section: Algorithms and Observablesmentioning

confidence: 99%

“…Later, we fix y 1 = −1 and ŷO to various values in the range −0.23 ≤ ŷO ≤ −0.25, and we obtain the estimate d B = 1.875 3 (6) by covering all the fitting results. Following the same procedure, we obtain the estimate d B = 1.874 7 (7) and ŷO = 0.135 (15) for B A , d B = 1.875 2 (7) and ŷO = 0.122(8) for B 1 . Thus, we expect (y O , ŷO ) is (15/8, 1/8) for B a and B 1 , and is (7/4, 1/4) for B 2 .…”

Section: Logarithmic Corrections For N =mentioning

confidence: 99%

“…The Potts model can be reformulated in graphical representations, including the Fortuin-Kasteleyn (FK) bond [3,4] and Q-flow (loop) representations [5,6]. Both the graphical representations can be obtained from the original spin representation by high-temperature expansion techniques, and, recently, these two graphical models are also directly mapped onto each other with the introduction of a loop-cluster joint model [7].…”

Section: Introductionmentioning

confidence: 99%

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Backbone and shortest-path exponents of the two-dimensional $Q$-state Potts model

Fang,

Ke,

Zhong

et al. 2021

Preprint

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We present a Monte Carlo study of the backbone and the shortest-path exponents of the twodimensional Q-state Potts model in the Fortuin-Kasteleyn bond representation. We first use cluster algorithms to simulate the critical Potts model on the square lattice and obtain the backbone exponents dB = 1.732 0(3) and 1.794(2) for Q = 2, 3 respectively. However, for large Q, the study suffers from serious critical slowing down and slowly converging finite-size corrections. To overcome these difficulties, we consider the O(n) loop model on the honeycomb lattice in the densely packed phase, which is regarded to correspond to the critical Potts model with Q = n 2 . With a highly efficient cluster algorithm, we determine from domains enclosed by the loops

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Section: Algorithms and Observablesmentioning

confidence: 99%

Section: Logarithmic Corrections For N =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Backbone and shortest-path exponents of the two-dimensional $Q$-state Potts model

Fang,

Ke,

Zhong

et al. 2021

Preprint

Self Cite

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show abstract

“…In 1972, Fortuin and Kasteleyn (FK) derived the socalled random-cluster (RC) representation [36] for the Q-state Potts model [37], in which the Ising and percolation models are simply the special cases for Q = 2 and Q → 1, respectively. This geometric representation has led to many exact results in 2D and efficient simulation algorithms as well [38][39][40][41]. A natural question arises: what is the upper critical dimension of the general RC model.…”

mentioning

confidence: 99%

“…First, what are the precise forms of logarithmic corrections in critical FK clusters at d c = 4 and d p = 6? Second, in the loop representation of the Ising model, which is another geometric representation and can be coupled to the RC model via the loop-cluster joint model [59], what would be geometric effects for d ≥ 4? Third, what are the upper critical dimensions for the general Q-state RC model?…”

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confidence: 99%

Geometric Upper Critical Dimensions of the Ising Model

Fang,

Zhou,

Deng

2022

Preprint

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The upper critical dimension of the Ising model is known to be dc = 4, above which critical behavior is regarded as trivial. We hereby argue that, in the random-cluster representation, the Ising model simultaneously exhibits two upper dimensions at (dc = 4, dp = 6), and critical clusters for d ≥ dp, except the largest one, are governed by exponents from percolation universality. We predict a rich variety of geometric properties and then provide strong evidences by extensive simulations in dimensions from 4 to 7 and on complete graphs. Our finding significantly advances the understanding of the Ising model, which is a fundamental system in many branches of physics.

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Geometric Upper Critical Dimensions of the Ising Model

Fang

Zhou

Deng

2022

Chinese Phys. Lett.

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The upper critical dimension of the Ising model is known to be d c = 4, above which critical behavior is regarded to be trivial. We hereby argue from extensive simulations that, in the random-cluster representation, the Ising model simultaneously exhibits two upper critical dimensions at (d c = 4, d p = 6), and critical clusters for d ≥ d p, except the largest one, are governed by exponents from percolation universality. We predict a rich variety of geometric properties and then provide strong evidence in dimensions from 4 to 7 and on complete graphs. Our findings significantly advance the understanding of the Ising model, which is a fundamental system in many branches of physics.

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Loop-Cluster Coupling and Algorithm for Classical Statistical Models

Cited by 9 publications

References 48 publications

Backbone and shortest-path exponents of the two-dimensional $Q$-state Potts model

Backbone and shortest-path exponents of the two-dimensional $Q$-state Potts model

Geometric Upper Critical Dimensions of the Ising Model

Geometric Upper Critical Dimensions of the Ising Model

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