General cluster Monte Carlo dynamics

Kandel, Daniel; Domany, Eytan

doi:10.1103/physrevb.43.8539

Cited by 105 publications

(100 citation statements)

References 16 publications

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“…Simply stated, the SW algorithm and other algorithms presented below are special cases of the dual Monte Carlo algorithm. 17,18) In a dual Monte Carlo algorithm, the Markov process alternates between two configuration spaces; the space of the original configurations that naturally arise from the model (such as the spin configurations in the Ising model and the world-line configurations in the quantum lattice models) and the space of the configurations of auxiliary variables. It is up to us to define the auxiliary variables and the resulting algorithm depends on the definition.…”

Section: Cluster Updatementioning

confidence: 99%

Recent Developments of World-Line Monte Carlo Methods

2004

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World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms -the loop algorithm, the worm algorithm, and the directedloop algorithm -for updating world-line configurations are presented in a unified perspective. Detailed descriptions of the algorithms in specific cases are also given.KEYWORDS: quantum spin system, Heisenberg model, quantum Monte Carlo, XY model, XXZ model, cluster algorithm, loop algorithm, worm algorithm, directed-loop algorithm, world-line method

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Section: Cluster Updatementioning

confidence: 99%

Recent Developments of World-Line Monte Carlo Methods

2004

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“…We consider the q-state Potts model as an example. With the framework of the dual algorithm [24,25], the partition function is expressed in the double summation over state S and graph G as…”

Section: Cluster-flip Flat Histogram Methodsmentioning

confidence: 99%

Novel Monte Carlo algorithms and their applications

Okabe

Tomita

Yamaguchi

2003

Physica A: Statistical Mechanics and its Applications

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We describe a generalized scheme for the probability-changing cluster (PCC) algorithm, based on the study of the finite-size scaling property of the correlation ratio, the ratio of the correlation functions with different distances. We apply this generalized PCC algorithm to the two-dimensional 6-state clock model. We also discuss the combination of the cluster algorithm and the extended ensemble method. We derive a rigorous broad histogram relation for the bond number. A Monte Carlo dynamics based on the number of potential moves for the bond number is proposed, and applied to the three-dimensional Ising and 3-state Potts models.

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“…The point of using this loop-cluster definition for the importance sampling of classical spin systems, as was treated rigorously in [17] [18], is that the sum over discrete steps in the probabilistic Markov chain, M, can then essentially be interchanged with the sum over discrete loop-clusters in the definition of the lattice partition function, which leads to more efficient numerical sampling. As was noticed in [15] and [16], however, when this loop-cluster definition of the new lattice configurations is applied to the Trotter-Suzuki formalism in (4), this definition has the advantage that closed loops on the D +1 dimensional lattice in (4) automatically preserve the definition of the trace.…”

Section: B Continuous-timementioning

confidence: 99%

The partition function zeroes of quantum critical points

Crompton¹

2009

Nuclear Physics B

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The Lee-Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity e h∆τ , and the Euclidean-time lattice spacing ∆τ can be divergent in the infrared (IR). We recently presented analytic arguments describing how a new space-Euclidean time zeroes expansion can be defined, which reproduces Lee and Yang's scaling but avoids the unresolved branch points associated with the breaking of nonlocal symmetries such as parity. We now present a first numerical analysis for this new zeros approach for a quantum spin chain system. We use our scheme to quantify the renormalization group flow of the physical lattice couplings to the IR fixed point of this system. We argue that the generic Finite-Size Scaling (FSS) function of our scheme is identically the entanglement entropy of the lattice partition function and, therefore, that we are able to directly extract the central charge, c, of the quantum spin chain system using conformal predictions for the scaling of the entanglement entropy.

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General cluster Monte Carlo dynamics

Cited by 105 publications

References 16 publications

Recent Developments of World-Line Monte Carlo Methods

Recent Developments of World-Line Monte Carlo Methods

Novel Monte Carlo algorithms and their applications

The partition function zeroes of quantum critical points

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