Nonuniversal critical dynamics in Monte Carlo simulations

Swendsen, Robert H.; Wang, Jian‐Sheng

doi:10.1103/physrevlett.58.86

Cited by 2,640 publications

(2,280 citation statements)

References 13 publications

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“…The concept of correlated bond percolation has been turned into a powerful Monte Carlo algorithm by Swendsen and Wang [5], and by Wolff [6], in which not individual spins are updated, but entire FK clusters. The main advantage of the nonlocal cluster update over a local spin update, like Metropolis or heat bath, is that it drastically reduces the critical slowing down near the critical point.…”

Section: Introductionmentioning

confidence: 99%

Geometrical vs. Fortuin–Kasteleyn clusters in the two-dimensional q-state Potts model

Janke

Schakel

2004

Nuclear Physics B

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The tricritical behavior of the two-dimensional q-state Potts model with vacancies for 0 ≤ q ≤ 4 is argued to be encoded in the fractal structure of the geometrical spin clusters of the pure model. The known close connection between the critical properties of the pure model and the tricritical properties of the diluted model is shown to be reflected in an intimate relation between Fortuin-Kasteleyn and geometrical clusters: The same transformation mapping the two critical regimes onto each other also maps the two cluster types onto each other. The map conserves the central charge, so that both cluster types are in the same universality class. The geometrical picture is supported by a Monte Carlo simulation of the high-temperature representation of the Ising model (q = 2) in which closed graph configurations are generated by means of a Metropolis update algorithm involving single plaquettes.

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Section: Introductionmentioning

confidence: 99%

Geometrical vs. Fortuin–Kasteleyn clusters in the two-dimensional q-state Potts model

Janke

Schakel

2004

Nuclear Physics B

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“…cluster update [10]. Instead of single spins, entire FK clusters are considered units to be flipped as a whole in this approach.…”

Section: E Swendsen-wang Cluster Updatementioning

confidence: 99%

Two-dimensional critical Potts and its tricritical shadow

Janke

Schakel

2006

Braz. J. Phys.

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These notes give examples of how suitably defined geometrical objects encode in their fractal structure thermal critical behavior. The emphasis is on the two-dimensional Potts model for which two types of spin clusters can be defined. Whereas the Fortuin-Kasteleyn clusters describe the standard critical behavior, the geometrical clusters describe the tricritical behavior that arises when including vacant sites in the pure Potts model. Other phase transitions that allow for a geometrical description discussed in these notes include the superfluid phase transition and Bose-Einstein condensation.

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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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Nonuniversal critical dynamics in Monte Carlo simulations

Cited by 2,640 publications

References 13 publications

Geometrical vs. Fortuin–Kasteleyn clusters in the two-dimensional q-state Potts model

Geometrical vs. Fortuin–Kasteleyn clusters in the two-dimensional q-state Potts model

Two-dimensional critical Potts and its tricritical shadow

The partition function zeroes of quantum critical points

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