We study a class of Monte Carlo algorithms for the nonlinear sigma-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 exists 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 sigma-model yield z(int,M2) = 1.5 +/- 0.5 (subjective 68% confidence interval), in agreement with our heuristic argument.
WOLFF-TYPE EMBEDDING ALGORITHMS FOR GENERAL NONLINEAR SIGMA-MODELS / S., Caracciolo; R. G., Edwards; Pelissetto, Andrea; A. D., Sokal. - In: NUCLEAR PHYSICS. B. - ISSN 0550-3213. - STAMPA. - 403:(1993), pp. 475-541. [10.1016/0550-3213(93)90044-p]
WOLFF-TYPE EMBEDDING ALGORITHMS FOR GENERAL NONLINEAR SIGMA-MODELS
PELISSETTO, Andrea;
1993
Abstract
We study a class of Monte Carlo algorithms for the nonlinear sigma-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 exists 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 sigma-model yield z(int,M2) = 1.5 +/- 0.5 (subjective 68% confidence interval), in agreement with our heuristic argument.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
