Multi-Grid Monte Carlo III. Two-Dimensional O(4)-Symmetric Nonlinear $σ$-Model

Details Multi-Grid Monte Carlo III. Two-Dimensional O(4)-Symmetric Nonlinear $σ$-Model Multi-Grid Monte Carlo III. Two-Dimensional O(4)-Symmetric Nonlinear $σ$-Model

1992-04-08

arxiv.org/abs/hep-lat/9112002v1

Nucl.Phys. B380 (1992) 621-664

Physics

High Energy Physics

High Energy Physics - Lattice

Scientific paper

10.1016/0550-3213(92)90262-A

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 nonlinear $\sigma$-model [= SU(2) principal chiral model], on lattices up to $256 \times 256$. We find a dynamic critical exponent $z_{int,{\cal M}^2} = 0.60 \pm 0.07$ for the W-cycle and $z_{int,{\cal M}^2} = 1.13 \pm 0.11$ for the V-cycle, compared to $z_{int,{\cal M}^2} = 2.0 \pm 0.15$ 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 $256 \times 256$ lattice, W-cycle MGMC is about 35 times as efficient as a single-site heat-bath algorithm.

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