Monte Carlo test of a hyperscaling relation for the two-dimensional self-avoiding walk. II

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.