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

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

1995-03-27

arxiv.org/abs/hep-lat/9503024v1

Phys.Rev. D53 (1996) 3438-3444

Physics

High Energy Physics

High Energy Physics - Lattice

377866 bytes Postscript, 16 pages, includes figures

Scientific paper

10.1103/PhysRevD.53.3438

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.

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