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

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

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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.

Original languageEnglish (US)
Pages (from-to)621-664
Number of pages44
JournalNuclear Physics, Section B
Volume380
Issue number3
DOIs
StatePublished - Aug 10 1992

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ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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