Multi-grid Monte Carlo (III). Two-dimensional O(4)-symmetric non-linear σ-model

Robert G. Edwards; Sabino JoséFerreira; Jonathan Goodman; Alan D. Sokal

doi:10.1016/0550-3213(92)90262-A

Multi-grid Monte Carlo (III). Two-dimensional O(4)-symmetric non-linear σ-model

Robert G. Edwards, Sabino JoséFerreira, Jonathan Goodman, Alan D. Sokal

Mathematics

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

Abstract

We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm with piecewise-constant interpolation applied to the two-dimensional O(4)-symmetric non-linear σ-model [ = SU(2) principal chirral model]], on lattices up to 256×256. We find a dynamic critical exponent z_int,M² = 0.60±0.07 for the W-cycle and z_{int,M² = 1.13±0.11} for the V-cycle, compared to z_int,M² = 2.0±0.15 for the single-site heat-bath algorithm (subjective 68% confidence intervals). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated. For a 256×256 lattice, W-cycle MGMC is about 35 times as efficient as a single-site heat-bath algorithm.

Original language	English (US)
Pages (from-to)	621-664
Number of pages	44
Journal	Nuclear Physics, Section B
Volume	380
Issue number	3
DOIs	https://doi.org/10.1016/0550-3213(92)90262-A
State	Published - Aug 10 1992

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/0550-3213(92)90262-A

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title = "Multi-grid Monte Carlo (III). Two-dimensional O(4)-symmetric non-linear σ-model",

abstract = "We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm with piecewise-constant interpolation applied to the two-dimensional O(4)-symmetric non-linear σ-model [ = SU(2) principal chirral model]], on lattices up to 256×256. We find a dynamic critical exponent zint,M2 = 0.60±0.07 for the W-cycle and zint,M2 = 1.13±0.11 for the V-cycle, compared to zint,M2 = 2.0±0.15 for the single-site heat-bath algorithm (subjective 68% confidence intervals). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated. For a 256×256 lattice, W-cycle MGMC is about 35 times as efficient as a single-site heat-bath algorithm.",

author = "Edwards, {Robert G.} and Sabino Jos{\'e}Ferreira and Jonathan Goodman and Sokal, {Alan D.}",

note = "Funding Information: computations reported here were carried out on the Cray Y-MP at the Pittsburgh Supercomputing Center (PSC). This work was supported in part by the US National Science Foundation grants DMS-8705599 and DMS-8911273 (J.G. and A.D.S.), by the US Department of Energy through contracts DE-FCO5-85ER250000 (R.G.E.) and DE-FGO2-90ER40581 (A.D.S.), and by PSC grant PHY890025P. One of the authors (S.J.F.) was supported by the Conselho Nacional de Pesquisas (Brazil), and another of the authors (J.G.) was partially supported by a Sloan Foundation Fellowship.",

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AU - Sokal, Alan D.

N1 - Funding Information: computations reported here were carried out on the Cray Y-MP at the Pittsburgh Supercomputing Center (PSC). This work was supported in part by the US National Science Foundation grants DMS-8705599 and DMS-8911273 (J.G. and A.D.S.), by the US Department of Energy through contracts DE-FCO5-85ER250000 (R.G.E.) and DE-FGO2-90ER40581 (A.D.S.), and by PSC grant PHY890025P. One of the authors (S.J.F.) was supported by the Conselho Nacional de Pesquisas (Brazil), and another of the authors (J.G.) was partially supported by a Sloan Foundation Fellowship.

PY - 1992/8/10

Y1 - 1992/8/10

N2 - We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm with piecewise-constant interpolation applied to the two-dimensional O(4)-symmetric non-linear σ-model [ = SU(2) principal chirral model]], on lattices up to 256×256. We find a dynamic critical exponent zint,M2 = 0.60±0.07 for the W-cycle and zint,M2 = 1.13±0.11 for the V-cycle, compared to zint,M2 = 2.0±0.15 for the single-site heat-bath algorithm (subjective 68% confidence intervals). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated. For a 256×256 lattice, W-cycle MGMC is about 35 times as efficient as a single-site heat-bath algorithm.

AB - We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm with piecewise-constant interpolation applied to the two-dimensional O(4)-symmetric non-linear σ-model [ = SU(2) principal chirral model]], on lattices up to 256×256. We find a dynamic critical exponent zint,M2 = 0.60±0.07 for the W-cycle and zint,M2 = 1.13±0.11 for the V-cycle, compared to zint,M2 = 2.0±0.15 for the single-site heat-bath algorithm (subjective 68% confidence intervals). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated. For a 256×256 lattice, W-cycle MGMC is about 35 times as efficient as a single-site heat-bath algorithm.

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Multi-grid Monte Carlo (III). Two-dimensional O(4)-symmetric non-linear σ-model

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