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

Abstract

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 -\ensuremath{\varepsilon}/${k}_{B}$${T}_{t}$=1.086\ifmmode\pm\else\textpm\fi{}0.002. The tricritical exponents of the trail shape and its free energy are, respectively, ${\ensuremath{\nu}}_{t}$=0.569\ifmmode\pm\else\textpm\fi{}0.008 and ${\ensuremath{\gamma}}_{t}$=1.133\ifmmode\pm\else\textpm\fi{}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 ${\ensuremath{\varphi}}_{t}$=0.807\ifmmode\pm\else\textpm\fi{}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\ensuremath{\le}${T}_{t}$) the persistence length appears to be \ensuremath{\sim}1.