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

Tereza Mendes·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 and a W-cycle, applied to the one-dimensional $O(4)$-symmetric nonlinear $σ$-model [= $SU(2)$ principal chiral model], on lattices from $L=128$ to $L=16384$. Our data for the integrated autocorrelation time $τ_{int,{\cal M}^2}$ are well fit by a logarithmic growth. We have no idea why the critical slowing-down is not completely eliminated.

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Tereza Mendes, Alan D. Sokal. 1995-03-27. Multi-Grid Monte Carlo. IV. One-Dimensional $O(4)$-Symmetric Nonlinear $σ$-Model. https://doi.org/10.1103/physrevd.53.3438

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