MONTE-CARLO TEST OF A HYPERSCALING RELATION FOR THE 2-DIMENSIONAL SELF-AVOIDING WALK .2.

By using a novel Monte Carlo algorithm which uses non-local moves to decrease the critical slowing-down, the authors simulate two-dimensional self-avoiding walks (SAWs) in a variable-length fixed-endpoint ensemble. This allows one to determine with reasonable accuracy the critical exponent alpha sing. As a byproduct, they obtain also accurate measurements of the exponent nu and the connective constant mu . They thus get a direct check of the hyperscaling relation dv=2- alpha sing. Estimates of alpha sing and mu are obtained by a maximum-likelihood fit which combines data generated at different fugacities.