Potts model formulation of branched polymers in a solvent

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Abstract
A Potts model formulation of the statistics of branched polymers or lattice animals in a solvent is given. The Migdal-Kadanoff renormalisation group is employed to study the critical behaviour or fractal dimension of the branched polymer. Four different critical behaviours are found, corresponding to random animal, collapse or theta point, percolation and compact cluster. The theta point behaviour is described by a tricritical point while percolation corresponds to a higher-order critical point, where the effect of the solvent on the branched polymer is the same as the screening effect of the other clusters in percolation.