Dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model

Jesús Salas; Alan D. Sokal

doi:10.1007/BF02174209

Dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model

Jesús Salas, Alan D. Sokal

Research output: Contribution to journal › Article › peer-review

Abstract

We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model. We find that the Li-Sokal bound on the autocorrelation time (τ_{int. δ} ≥ const × C_H) holds along the self-dual curve of the symmetric Ashkin-Teller model, and is almost, but not quite sharp. The ratio τ_{int. δ} /C_H appears to tend to infinity either as a logarithm or as a small power (0.05 ≤ p ≤ 0.12). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.

Original language	English (US)
Pages (from-to)	297-361
Number of pages	65
Journal	Journal of Statistical Physics
Volume	85
Issue number	3-4
DOIs	https://doi.org/10.1007/BF02174209
State	Published - Nov 1996

Keywords

Ashkin-Teller model
Autocorrelation time
Cluster algorithm
Critical slowing down
Dynamical critical behavior
Fitting correlated data
Ising model
Li-Sokal bound
Monte Carlo
Potts model
Swendsen-Wang algorithm

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02174209

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title = "Dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model",

abstract = "We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model. We find that the Li-Sokal bound on the autocorrelation time (τint. δ ≥ const × CH) holds along the self-dual curve of the symmetric Ashkin-Teller model, and is almost, but not quite sharp. The ratio τint. δ /CH appears to tend to infinity either as a logarithm or as a small power (0.05 ≤ p ≤ 0.12). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.",

keywords = "Ashkin-Teller model, Autocorrelation time, Cluster algorithm, Critical slowing down, Dynamical critical behavior, Fitting correlated data, Ising model, Li-Sokal bound, Monte Carlo, Potts model, Swendsen-Wang algorithm",

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year = "1996",

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T1 - Dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model

AU - Salas, Jesús

AU - Sokal, Alan D.

PY - 1996/11

Y1 - 1996/11

N2 - We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model. We find that the Li-Sokal bound on the autocorrelation time (τint. δ ≥ const × CH) holds along the self-dual curve of the symmetric Ashkin-Teller model, and is almost, but not quite sharp. The ratio τint. δ /CH appears to tend to infinity either as a logarithm or as a small power (0.05 ≤ p ≤ 0.12). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.

AB - We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model. We find that the Li-Sokal bound on the autocorrelation time (τint. δ ≥ const × CH) holds along the self-dual curve of the symmetric Ashkin-Teller model, and is almost, but not quite sharp. The ratio τint. δ /CH appears to tend to infinity either as a logarithm or as a small power (0.05 ≤ p ≤ 0.12). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.

KW - Ashkin-Teller model

KW - Autocorrelation time

KW - Cluster algorithm

KW - Critical slowing down

KW - Dynamical critical behavior

KW - Fitting correlated data

KW - Ising model

KW - Li-Sokal bound

KW - Monte Carlo

KW - Potts model

KW - Swendsen-Wang algorithm

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Dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model

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Keywords

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