Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain

A.A. Nazarov   ; S. A. Paston

Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 2, pp. 262-283

Résumé

We consider the dimer model on a hexagonal lattice. This model can be represented as a "pile of cubes in a box." The energy of a configuration is given by the volume of the pile. The partition function is computed by the classical MacMahon formula or as the determinant of the Kasteleyn matrix. We use the MacMahon formula to derive the scaling behavior of free energy in the limit as the lattice spacing goes to zero and temperature goes to infinity. We consider the case of a finite hexagonal domain, the case where one side of the hexagonal box is infinite, and the case of inhomogeneous Boltzmann weights. We obtain an asymptotic expansion of free energy, which is called finite-size corrections, and discuss the universality and physical meaning of the expansion coefficients.

Détail

Mots-clés : dimer, hexagonal lattice.
Keywords: limit shape, free energy scaling, finite-size correction, scaling limit

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