Year: 2025
Type: article
Abstract: The exact finite-size corrections to the free energy F of the dimer model on lattice M × N with cylindrical boundary conditions have been derived for three cases where the lattice is completely covered by dimers: M = 2 M , N = 2 N ; M = 2 M − 1 , N = 2 N ; and M = 2 M , N = 2 N − 1 . For these types of cylinders, ratios r p (ρ) of the pth coefficient of F have been calculated for the infinitely long cylinder ( M → ∞ ) and infinitely long strip ( N → ∞ ) at varying aspect ratios. As in previous studies of the dimer model on the rectangular lattice with free boundary conditions and for the Ising model with Brascamp-Kunz boundary conditions, the limiting values p → ∞ exhibit abrupt anomalous behaviour of ratios r p (ρ) at certain values of ρ. These critical values of ρ and the limiting values of the finite-size expansion coefficient ratios vary between the different models.
Source: Physica Scripta
Author: Vladimir V Papoyan
Institutions: Joint Institute for Nuclear Research, Dubna State University
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408230940