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, at least for an asymptotically free model, such an algorithm can have a 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 exist only if the manifold is a discrete quotient of a product of spheres. Numerical simulations of the idealized codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield zint,M2 = 1.5±0.5 (sujective 68% confidence interval), in agreement with our heuristic argument.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 475-541 |
| Number of pages | 67 |
| Journal | Nuclear Physics, Section B |
| Volume | 403 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - Aug 16 1993 |
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ASJC Scopus subject areas
- Nuclear and High Energy Physics
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Wolff-type embedding algorithms for general nonlinear σ-models. / Caracciolo, Sergio; Edwards, Robert G.; Pelissetto, Andrea; Sokal, Alan D.
In: Nuclear Physics, Section B, Vol. 403, No. 1-2, 16.08.1993, p. 475-541.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Wolff-type embedding algorithms for general nonlinear σ-models
AU - Caracciolo, Sergio
AU - Edwards, Robert G.
AU - Pelissetto, Andrea
AU - Sokal, Alan D.
PY - 1993/8/16
Y1 - 1993/8/16
N2 - 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, at least for an asymptotically free model, such an algorithm can have a 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 exist only if the manifold is a discrete quotient of a product of spheres. Numerical simulations of the idealized codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield zint,M2 = 1.5±0.5 (sujective 68% confidence interval), in agreement with our heuristic argument.
AB - 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, at least for an asymptotically free model, such an algorithm can have a 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 exist only if the manifold is a discrete quotient of a product of spheres. Numerical simulations of the idealized codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield zint,M2 = 1.5±0.5 (sujective 68% confidence interval), in agreement with our heuristic argument.
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U2 - 10.1016/0550-3213(93)90044-P
DO - 10.1016/0550-3213(93)90044-P
M3 - Article
VL - 403
SP - 475
EP - 541
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
IS - 1-2
ER -