Computer simulation of trails on a square lattice. II. Finite temperatures and the collapse transition

We study by the scanning simulation method trails on a square lattice at finite temperatures. This method constitutes a very efficient tool since it enables one to obtain results at many temperatures from a single sample generated at any given temperature. The tricritical temperature at which the collapse transition occurs is -epsilon-c/k/sub B/T/sub t/ = 1.086 +- 0.002. The tricritical exponents of the trail shape and its free energy are, respectively, ν/sub t/ = 0.569 +- 0.008 and γ/sub t/ = 1.133 +- 0.024 (95% confidence limits). They are equal within the error bars to the exact values of self-attracting self-avoiding walks (SAW's). However, the crossover exponent phi/sub t/ = 0.807 +- 0.005 is significantly larger than the exact value 0.423 of SAW's. We also carry out a detailed scaling analysis near T/sub t/ and demonstrate that the various properties scale as predicted by theory. At sufficiently low temperatures (T≤T/sub t/) the persistence length appears to be /similar to/1