MONTE-CARLO STUDY OF THE THETA-POINT FOR COLLAPSING TREES

We investigate the collapse transition of lattice trees with nearest n eighbor attraction in two and three dimensions. Two methods are used: (1) A stochastic optimization process of the Robbins-Monro type, which is designed solely to locate the maximum value of the specific heat; and (2) umbrella sampling, which is designed to sample data over a wid e temperature range, as well as to combat the quasiergodicity of Metro polis algorithms in the collapsed phase. We find good evidence that th e transition is second order with a divergent specific heat, and that the divergence of the specific heat coincides with the metric collapse .