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 -{ε}/kB{T}ₜ=1.086±0.002. The tricritical exponents of the trail shape and its free energy are, respectively,{{ν}}ₜ=0.569±0.008 and{{γ}}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 φₜ=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 Tₜ and demonstrate that the various properties scale as predicted by theory. At sufficiently low temperatures (T{≤}Tₜ) the persistence length appears to be {~}1.