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Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain. / Nazarov, A. A.; Paston, S. A.

In: Theoretical and Mathematical Physics(Russian Federation), Vol. 205, No. 2, 11.2020, p. 1473-1491.

Research output: Contribution to journal › Article › peer-review

Harvard

Nazarov, AA & Paston, SA 2020, 'Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain', Theoretical and Mathematical Physics(Russian Federation), vol. 205, no. 2, pp. 1473-1491. https://doi.org/10.1134/S0040577920110069

APA

Nazarov, A. A., & Paston, S. A. (2020). Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain. Theoretical and Mathematical Physics(Russian Federation), 205(2), 1473-1491. https://doi.org/10.1134/S0040577920110069

Vancouver

Nazarov AA, Paston SA. Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain. Theoretical and Mathematical Physics(Russian Federation). 2020 Nov;205(2):1473-1491. https://doi.org/10.1134/S0040577920110069

Author

Nazarov, A. A. ; Paston, S. A. / Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain. In: Theoretical and Mathematical Physics(Russian Federation). 2020 ; Vol. 205, No. 2. pp. 1473-1491.

BibTeX

@article{c33e8a3e5c6f4832a891b3c2f890e2cd,
title = "Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain",
abstract = "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.",
keywords = "dimer, finite-size correction, free energy scaling, hexagonal lattice, limit shape, scaling limit, TILINGS, 6-VERTEX MODEL, LATTICE",
author = "Nazarov, {A. A.} and Paston, {S. A.}",
note = "Funding Information: This research is supported by the Russian Foundation for Basic Research (Grant No. 18-01-00916). Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = nov,
doi = "10.1134/S0040577920110069",
language = "English",
volume = "205",
pages = "1473--1491",
journal = "Theoretical and Mathematical Physics",
issn = "0040-5779",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain

AU - Nazarov, A. A.

AU - Paston, S. A.

N1 - Funding Information: This research is supported by the Russian Foundation for Basic Research (Grant No. 18-01-00916). Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/11

Y1 - 2020/11

N2 - 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.

AB - 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.

KW - dimer

KW - finite-size correction

KW - free energy scaling

KW - hexagonal lattice

KW - limit shape

KW - scaling limit

KW - TILINGS

KW - 6-VERTEX MODEL

KW - LATTICE

UR - http://www.scopus.com/inward/record.url?scp=85096532628&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/ebbd15bd-edf5-31ca-bd51-c1031fc7f5e8/

U2 - 10.1134/S0040577920110069

DO - 10.1134/S0040577920110069

M3 - Article

AN - SCOPUS:85096532628

VL - 205

SP - 1473

EP - 1491

JO - Theoretical and Mathematical Physics

JF - Theoretical and Mathematical Physics

SN - 0040-5779

IS - 2

ER -

ID: 71363685