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

Tereza Mendes; Alan D. Sokal

doi:10.1103/PhysRevD.53.3438

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

High Energy Physics - Lattice 2009-10-28 v1

Authors: 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 $\sigma$ -model [= $SU(2)$ principal chiral model], on lattices from $L=128$ to $L=16384$ . Our data for the integrated autocorrelation time $\tau_{int,{\cal M}^2}$ are well fit by a logarithmic growth. We have no idea why the critical slowing-down is not completely eliminated.

Keywords

multi-grid Monte Carlo O(4) nonlinear sigma model critical slowing down autocorrelation time

Cite

@article{arxiv.hep-lat/9503024,
  title  = {Multi-Grid Monte Carlo. IV. One-Dimensional $O(4)$-Symmetric Nonlinear $\sigma$-Model},
  author = {Tereza Mendes and Alan D. Sokal},
  journal= {arXiv preprint arXiv:hep-lat/9503024},
  year   = {2009}
}

Comments

377866 bytes Postscript, 16 pages, includes figures

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