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.
ASJC Scopus subject areas
- Nuclear and High Energy Physics