@article{6434d735cef54959affa8b82859e2b67,

title = "Wolff-type embedding algorithms for general nonlinear σ-models",

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.",

author = "Sergio Caracciolo and Edwards, {Robert G.} and Andrea Pelissetto and Sokal, {Alan D.}",

note = "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 Podest{\`a} 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{\textquoteright} 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.).",

year = "1993",

month = aug,

day = "16",

doi = "10.1016/0550-3213(93)90044-P",

language = "English (US)",

volume = "403",

pages = "475--541",

journal = "Nuclear Physics B",

issn = "0550-3213",

publisher = "Elsevier",

number = "1-2",

}