Abstract
The partially directed compact lattice animal model on the square lattice is solved exactly for the cluster number and average cluster radius along the directed axis in terms of the appropriate generating functions. For the critical exponents we findθ=0 andυ ‖=1. Caliper size distribution along the directed axis is also calculated analytically. It is used to confirmυ ‖=1 and to study some finite-size scaling properties for this model. For the perpendicular cluster radius distribution, a combination of analytic arguments and computer results leads to a conjecture on the exact form of the appropriate generating function and to the resultυ ⊥=1/2. Some calculations are reported for the triangular lattice and for hypercubic lattices ind>2.
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Forgacs, G., Privman, V. Directed compact lattice animals: Exact results. J Stat Phys 49, 1165–1180 (1987). https://doi.org/10.1007/BF01017564
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DOI: https://doi.org/10.1007/BF01017564