Mendes, T; Pelissetto, A; Sokal, AD; (1996) Multi-grid Monte Carlo via XY embedding. General theory and two-dimensional O(N)-symmetric non-linear sigma-models. **NUCL PHYS B** , 477 (1) 203 - 270.

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## Abstract

We introduce a variant of the multi-grid Monte Carlo (MGMC) method, based on the embedding of an XY model into the target model, and we study its mathematical properties for a variety of non-linear sigma-models, We then apply the method to the two-dimensional O(N)-symmetric non-linear sigma-models (also called N-vector models) with N = 3,4,8 and study its dynamic critical behavior. Using lattices up to 256 x 256, we find dynamic critical exponents z(int,M2) approximate to 0.70 +/- 0.08, 0.60 +/- 0.07, 0.52 +/- 0.10 for N = 3,4, 8, respectively (subjective 68% confidence intervals). Thus, for these asymptotically free models, critical slowing down is greatly reduced compared to local algorithms, but not completely eliminated; and the dynamic critical exponent does apparently vary with N. We also analyze the static data for N = 8 using a finite-size scaling extrapolation method. The correlation length xi agrees with the four-loop asymptotic-freedom prediction to within approximate to 1% over the interval 12 less than or similar to xi less than or similar to 650.

Type: | Article |
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Title: | Multi-grid Monte Carlo via XY embedding. General theory and two-dimensional O(N)-symmetric non-linear sigma-models |

Keywords: | multi-grid Monte Carlo, XY embedding, critical slowing down, finite-size-scaling analysis, ACCELERATED STOCHASTIC ALGORITHMS, ASYMPTOTICALLY FREE THEORIES, LATTICE PERTURBATION-THEORY, U(1) GAUGE-FIELDS, EXACT MASS GAP, COUPLING-CONSTANT, SCALING BEHAVIOR, 4 DIMENSIONS, O(3), SIMULATIONS |

UCL classification: | UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics |

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