Asymptotics of block toeplitz determinants and the classical dimer model

We compute the asymptotics of a block Toeplitz determinant which arises in the classical dimer model for the triangular lattice when considering the monomer-monomer correlation function. The model depends on a parameter interpolating between the square lattice (t = 0) and the triangular lattice (t = 1), and we obtain the asymptotics for 0 < t <= 1. For 0 < t < 1 we apply the Szego Limit Theorem for block Toeplitz determinants. The main difficulty is to evaluate the constant term in the asymptotics, which is generally given only in a rather abstract form.