CLUSTER ALGORITHMS FOR NONLINEAR SIGMA MODELS

Percolation cluster Monte Carlo algorithms for nonlinear σ-models on the lattice are reviewed with special emphasis on their possible generalizations. While they have been found to practically eliminate critical slowing down for the standard O(n) invariant vector models, their extension to other physically similar models — like RPn−1 and SU(n)×SU(n) chiral models — is less straight forward than one might have thought. I outline the present situation in this area of research. In the second part of my talk I described a numerical calculation of a physical running coupling constant in the O(3) model. This represents an application of the cluster technique in a preparatory study for a later lattice gauge theory calculation. This material can be found in Ref. 11.