TY - JOUR

T1 - Multi-grid Monte Carlo (III). Two-dimensional O(4)-symmetric non-linear σ-model

AU - Edwards, Robert G.

AU - JoséFerreira, Sabino

AU - Goodman, Jonathan

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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U2 - 10.1016/0550-3213(92)90262-A

DO - 10.1016/0550-3213(92)90262-A

M3 - Article

AN - SCOPUS:0000100917

SN - 0550-3213

VL - 380

SP - 621

EP - 664

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

ER -