Compact polymers on decorated square lattices
نویسنده
چکیده
A Hamiltonian cycle of a graph is a closed path that visits every vertex once and only once. It serves as a model of a compact polymer on a lattice. I study the number of Hamiltonian cycles, or equivalently the entropy of a compact polymer, on various lattices that are not necessarily homogeneous. Estimates for the number are obtained by two methods. One is the saddle point approximation for a field theoretic representation. The other is the numerical diagonalization of the transfer matrix of a fully packed loop model in the zero fugacity limit. In the latter method, several scaling exponents are also obtained. PACS: 05.20.-y, 02.10.Eb, 05.50.+q, 82.35.+t
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