Abstract:
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.
Citation:
A.A. Nazarov, S. A. Paston, “Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain”, TMF, 205:2 (2020), 262–283; Theoret. and Math. Phys., 205:2 (2020), 1473–1491
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\by A.A.~Nazarov, S.~A.~Paston
\paper Finite-size correction to the~scaling of free energy in the~dimer model on a~hexagonal domain
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\pages 262--283
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\jour Theoret. and Math. Phys.
\yr 2020
\vol 205
\issue 2
\pages 1473--1491
\crossref{https://doi.org/10.1134/S0040577920110069}
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Linking options:
https://www.mathnet.ru/eng/tmf9874
https://doi.org/10.4213/tmf9874
https://www.mathnet.ru/eng/tmf/v205/i2/p262
This publication is cited in the following 1 articles:
Ivan N. Burenev, Andrei G. Pronko, “Thermodynamics of the Five-Vertex Model with Scalar-Product Boundary Conditions”, Commun. Math. Phys., 405:6 (2024)
Citation in format AMSBIB
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