Dynamic critical behavior of the Swendsen - Wang algorithm for the three-dimensional Ising model

Giovanni Ossola; Alan D. Sokal

doi:10.1016/j.nuclphysb.2004.04.026

Dynamic critical behavior of the Swendsen - Wang algorithm for the three-dimensional Ising model

Giovanni Ossola, Alan D. Sokal

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

Abstract

We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the three-dimensional Ising model at the critical point. For the dynamic critical exponents associated to the integrated autocorrelation times of the "energy-like" observables, we find z_int,N=z_int,E= z_int,E′=0.459±0.005±0.025, where the first error bar represents statistical error (68% confidence interval) and the second error bar represents possible systematic error due to corrections to scaling (68% subjective confidence interval). For the "susceptibility-like" observables, we find z_int,M²=z_int, S₂=0.443±0.005±0.030. For the dynamic critical exponent associated to the exponential autocorrelation time, we find z_exp≈0.481. Our data are consistent with the Coddington-Baillie conjecture z_SW=β/ν≈0.5183, especially if it is interpreted as referring to z_exp.

Original language	English (US)
Pages (from-to)	259-291
Number of pages	33
Journal	Nuclear Physics B
Volume	691
Issue number	3
DOIs	https://doi.org/10.1016/j.nuclphysb.2004.04.026
State	Published - Jul 26 2004

Keywords

Autocorrelation time
Cluster algorithm
Dynamic critical exponent
Ising model
Monte Carlo
Potts model
Swendsen-Wang algorithm

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/j.nuclphysb.2004.04.026

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@article{f927e0fa815740bca3da61878e0d43c0,

title = "Dynamic critical behavior of the Swendsen - Wang algorithm for the three-dimensional Ising model",

abstract = "We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the three-dimensional Ising model at the critical point. For the dynamic critical exponents associated to the integrated autocorrelation times of the {"}energy-like{"} observables, we find zint,N=zint,E= zint,E′=0.459±0.005±0.025, where the first error bar represents statistical error (68% confidence interval) and the second error bar represents possible systematic error due to corrections to scaling (68% subjective confidence interval). For the {"}susceptibility-like{"} observables, we find zint,M2=zint, S2=0.443±0.005±0.030. For the dynamic critical exponent associated to the exponential autocorrelation time, we find zexp≈0.481. Our data are consistent with the Coddington-Baillie conjecture zSW=β/ν≈0.5183, especially if it is interpreted as referring to zexp.",

keywords = "Autocorrelation time, Cluster algorithm, Dynamic critical exponent, Ising model, Monte Carlo, Potts model, Swendsen-Wang algorithm",

author = "Giovanni Ossola and Sokal, {Alan D.}",

note = "Funding Information: This research was supported in part by U.S. National Science Foundation Grants PHY-0099393 and PHY-0116590.",

year = "2004",

month = jul,

day = "26",

doi = "10.1016/j.nuclphysb.2004.04.026",

language = "English (US)",

volume = "691",

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T1 - Dynamic critical behavior of the Swendsen - Wang algorithm for the three-dimensional Ising model

AU - Ossola, Giovanni

AU - Sokal, Alan D.

N1 - Funding Information: This research was supported in part by U.S. National Science Foundation Grants PHY-0099393 and PHY-0116590.

PY - 2004/7/26

Y1 - 2004/7/26

N2 - We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the three-dimensional Ising model at the critical point. For the dynamic critical exponents associated to the integrated autocorrelation times of the "energy-like" observables, we find zint,N=zint,E= zint,E′=0.459±0.005±0.025, where the first error bar represents statistical error (68% confidence interval) and the second error bar represents possible systematic error due to corrections to scaling (68% subjective confidence interval). For the "susceptibility-like" observables, we find zint,M2=zint, S2=0.443±0.005±0.030. For the dynamic critical exponent associated to the exponential autocorrelation time, we find zexp≈0.481. Our data are consistent with the Coddington-Baillie conjecture zSW=β/ν≈0.5183, especially if it is interpreted as referring to zexp.

AB - We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the three-dimensional Ising model at the critical point. For the dynamic critical exponents associated to the integrated autocorrelation times of the "energy-like" observables, we find zint,N=zint,E= zint,E′=0.459±0.005±0.025, where the first error bar represents statistical error (68% confidence interval) and the second error bar represents possible systematic error due to corrections to scaling (68% subjective confidence interval). For the "susceptibility-like" observables, we find zint,M2=zint, S2=0.443±0.005±0.030. For the dynamic critical exponent associated to the exponential autocorrelation time, we find zexp≈0.481. Our data are consistent with the Coddington-Baillie conjecture zSW=β/ν≈0.5183, especially if it is interpreted as referring to zexp.

KW - Autocorrelation time

KW - Cluster algorithm

KW - Dynamic critical exponent

KW - Ising model

KW - Monte Carlo

KW - Potts model

KW - Swendsen-Wang algorithm

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EP - 291

JO - Nuclear Physics B

JF - Nuclear Physics B

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Dynamic critical behavior of the Swendsen - Wang algorithm for the three-dimensional Ising model

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