Collapsing animals

Lattice animals with fugacities conjugate to the number of independent cycl es, or to the number of nearest neighbour contacts, go through a collapse t ransition at a theta-point at a critical value of the fugacity. We examine the phase diagram of a model which includes both a cycle and a contact fuga city with Monte Carlo methods. Using an underlying cut-and-paste Metropolis algorithm for lattice animals, we implement in the first instance a multip le Markov chain simulation of collapsing animals to estimate the location o f the collapse transitions and the values of the crossover exponents associ ated with these. Secondly, we use umbrella sampling to sample animals over a rectangle in the phase diagram to examine the structure of the phase diag ram of these animals.