Universality classes of theθandθ’points

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Abstract
We address the problem of obtaining reliable statistical information on two tricritical points of recent interest, the θ point (conventionally modeled by the self-avoiding walk with nearest-neighbor attractive interactions) and the θ’ 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 θ and θ’ 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 θ and θ’ points belong to distinct universality classes.