We address the question of the dependence of the bulk free energy on boundary conditions
for the six-vertex model. Here we compare the bulk free energy for periodic and domain wall …

We propose an architecture based on superconducting qubits and resonators for the
implementation of a variety of exotic lattice systems, such as spin and Hubbard models in …

We consider the domino tilings of an Aztec diamond with a cut-off corner of macroscopic
square shape and given size and address the bulk properties of tilings as the size is varied …

Closed-form expressions are obtained for the partition function of the Ising model on an M×
N simple-quartic lattice embedded on a Möbius strip and a Klein bottle. The solutions all …

We consider the problem of enumerating spanning trees on lattices. Closed-form
expressions are obtained for the spanning tree generating function for a hypercubic lattice in …

We express the partition functions of the dimer model on finite square lattices under five
different boundary conditions (free, cylindrical, toroidal, Möbius strip, and Klein bottle) …

For the free models of statistical mechanics on torus, including the Ising model, dimer model
and Gaussian model, exact asymptotic expansions of free energy, internal energy and …

In chemical graph theory, various topological indices of the hexagonal lattices such as the
energy, the numbers of perfect matchings and spanning trees, and so on, have been studied …

We study the finite-size scaling properties of the Ising model on the Möbius strip and the
Klein bottle. The results are compared with those of the Ising model under different boundary …

A seminal milestone in lattice statistics is the exact solution of the enumeration of dimers on
a simple-quartic net obtained by Fisher, Kasteleyn, and Temperley (FKT) in 1961. An …