ar X iv : h ep - l at / 9 20 50 05 v 1 4 M ay 1 99 2 Wolff - Type Embedding Algorithms for General Nonlinear σ -

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 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 σ-model yield zint,M2 = 1.5 ± 0.5 (subjective 68% confidence interval), in agreement with our heuristic argument. Submitted to Nuclear Physics B.