STATISTICS OF COLLAPSED LATTICE ANIMALS - RIGOROUS RESULTS AND MONTE-CARLO SIMULATIONS

In this paper a two-dimensional model of collapsed lattice animals wit h nearest-neighbour contact interactions is introduced and the limitin g free energy for the model is proved to exist. We also establish that the partition function for collapsed lattice animals is related to th e reliability polynomial for the m x m grid graph and to the generatin g function for spanning forests on the m x m grid graph. From these re lationships and using results about directed animals we are able to ob tain rigorous upper and lower bounds on the free energy for collapsed lattice animals. In addition we present Monte Carlo evidence that the heat capacity associated with this model remains bounded in the thermo dynamic limit. In fact we do not find any evidence for a second-order phase transition for collapsed lattice animals.