The growing self-avoiding trail

Abstract

The author introduces a new random walk which can be used as a model for the theta polymer. The walk belongs to a different universality class from the usual SAW. Extensive Monte Carlo calculations have been performed to calculate the exponents gamma and nu . The author finds in two dimensions nu -0.535 and gamma =1.025 and in three dimensions nu =0.50 and gamma =1.0. This result strongly suggests that the upper critical dimension is equal to three.