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 -ɛ/$k_B$ $T_t$=1.086±0.002. The tricritical exponents of the trail shape and its free energy are, respectively, ${\nu }_t$=0.569±0.008 and ${\gamma }_t$=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 ${\phi }_t$=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 $T_t$ and demonstrate that the various properties scale as predicted by theory. At sufficiently low temperatures (T≤$T_t$) the persistence length appears to be ∼1.