WOLFF-TYPE EMBEDDING ALGORITHMS FOR GENERAL NONLINEAR SIGMA-MODELS

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.