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
.