Tricritical exponents for trails on a square lattice obtained by the scanning simulation method

A trail is a lattice chain model which is allowed to self-intersect while an overlap of two bonds is forbidden. With each intersection is associated an attractive interaction energy, which gives rise to a transition from swollen to collapsed structures at a certain tricritical temperature. We study the tricritical behavior of trails on a square lattice using the scanning simulation method, which is especially efficient for this problem. The interesting question is whether trails and self-avoiding walks (SAW's) belong to the same universality class. In the present calculation, the shape exponent vₜ and the free-energy exponent γₜ for trails at the tricritical point are found to be equal (within the statistical error) to the corresponding values derived analytically (and conjectured to be exact) for self-attracting SAW's. However, our value for the crossover exponent φₜ is significantly larger than the exact value of self-attracting SAW's.