Universality classes of the theta and theta ' points.

Abstract

We address the problem of obtaining reliable statistical information on two tricritical points of recent interest, the \ensuremath{\theta} point (conventionally modeled by the self-avoiding walk with nearest-neighbor attractive interactions) and the \ensuremath{\theta}' point (the self-avoiding walk with nearest-neighbor interactions and a subset of the next-nearest-neighbor interactions). Specifically, we show how two very special walk algorithms can provide sufficient statistical information to elucidate fully the multicritical properties. We carry out a Monte Carlo calculation of the exponents at the \ensuremath{\theta} and \ensuremath{\theta}' points using these special walk algorithms. We also examine the crossover behavior along a critical surface that contains both points. Our numerical results suggest that the universality class is changing continuously along this critical surface, so that the \ensuremath{\theta} and \ensuremath{\theta}' points belong to distinct universality classes.