Abstract
We study a class of Monte Carlo algorithms for the nonlinear σ-model, based on a Wolff-type embedding of Ising spins into the target manifold M. We argue heuristically that such an algorithm can have dynamic critical exponent z ≪ 2 only if the embedding is based on an involutive isometry of M whose fixed-point manifold has codimension 1. Such an isometry exists only if the manifold is a product of spheres and discrete quotients of spheres. Numerical simulations of the codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield z = 1.5 ± 0.3, in agreement with our heuristic argument.
Original language | English (US) |
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Pages (from-to) | 72-75 |
Number of pages | 4 |
Journal | Nuclear Physics B (Proceedings Supplements) |
Volume | 20 |
Issue number | C |
DOIs | |
State | Published - May 20 1991 |
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics