Directed compact lattice animals, restricted partitions of an integer, and the infinite-state Potts model.
نویسندگان
چکیده
We consider a directed compact site lattice animal problem on the d-dimensional hypercubic lattice, and establish its equivalence with (i) the infinite-state Potts model and (ii) the enumeration of sd 2 1ddimensional restricted partitions of an integer. The directed compact lattice animal problem is solved exactly in d 2, 3 using known solutions of the enumeration problem. The maximum number of lattice animals of size n grows as expscnsd21dydd. Also, the infinite-state Potts model solution leads to a conjectured limiting form for the generating function of restricted partitions for d . 3, the latter an unsolved problem in number theory.
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عنوان ژورنال:
- Physical review letters
دوره 76 2 شماره
صفحات -
تاریخ انتشار 1996