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.

N1 - Funding Information:
We wish to thank Richard Brower, Ferenc Niedermayer, Claudio Parrinello and Ulli Wolff for helpful discussions about embedding algorithms, and Oliver Attic, Sylvain Cappell and Fabio Podestà for helpful discussions about topology and geometry. The computations reported here were carried out on a loosely coupled MIMD parallel computer (with local memory and message-passing communication via Internet/ Bitnet/ Decnet and four neural networks) consisting of the following processors: the Cray X-MP at CRTN-ENEL (Pisa); the Cray Y-MP at CINECA (Bologna); the Cray Y-MP at the Pittsburgh Supercomputing Center; the Cyber 205 at the John von Neumann Supercomputer Center; ansi the ETA-lOG, ETA-100, Cray Y-MP, Silicon Graphics 4D/24OGTX and numerous DECstation 5000, IBM RS-6000/320 and IBM RS-6000/530 workstations at SCRI (Tallahassee). We thank all these organizations for their generous contribution to this research. The authors’ research was supported in part by the Istituto Nazionale di Fisica Nucleare (S.C. and A.P.), U.S. Department of Energy contract DE-FCO5-85ER250000 (R.G.E.), U.S. Department of Energy contract DE-FGO2-90ER40581 (A.D.S.), U.S. National Science Foundation grants DMS-8705599 and DMS-8911273 (A.D.S.), and NATO Collaborative Research Grant CRG 910251 (S.C. and A.D.S.).

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

AN - SCOPUS:0000852610

SN - 0550-3213

VL - 403

SP - 475

EP - 541

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 1-2

ER -