Exact partition functions and correlation functions of multiple Hamiltonian walks on the Manhattan lattice

This is a general and exact study of multiple Hamiltonian walks (HAW) filling the two-dimensional (2D) Manhattan lattice. We generalize the original exact solution for a single HAW by Kasteleyn to a system of multiple closed walks, aimed at modeling a polymer melt. In 2D, two basic nonequivalent topological situations are distinguished. (1) the Hamiltonian loops are all rooted and contractible to a point: adjacent one to another and, on a torus, homotopic to zero, (2) the loops can encircle one another and, on a torus, can wind around it