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Asymptotics of block Toeplitz determinants and the classical dimer model

Estelle L. Basor·Torsten Ehrhardt
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Abstract

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 $0<t\le 1$. For $0<t<1$ we apply the Szegö 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.

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Estelle L. Basor, Torsten Ehrhardt. 2006-07-28. Asymptotics of block Toeplitz determinants and the classical dimer model. https://doi.org/10.1007/s00220-007-0276-5

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