Saburo Higuchi 1999 J. Phys. A: Math. Gen. 32 3697 doi:10.1088/0305-4470/32/20/303
Saburo Higuchi
Show affiliationsA 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 homogeneous but with a sublattice structure. 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.
82B30 Statistical thermodynamics (See also 80-XX)
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
Issue 20 (21 May 1999)
Received 7 December 1998
Saburo Higuchi 1999 J. Phys. A: Math. Gen. 32 3697
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