Approximate thermodynamics of the two-dimensional Ising model in an external magnetic field
Year: 2025
Type: article
Abstract: We introduce approximate expressions for the thermodynamics of the two-dimensional Ising model in an external magnetic field. The external field breaks the system’s symmetry, which complicates the exact calculation of the free energy. To address this, we write the model in its quaternion representation to apply a small angle approximation with respect to a reference frame. The approximation simplifies the transfer matrix to a centrosymmetric matrix for which the largest eigenvalue is known and depends on the external field strength. We therefore write an approximate expression for the system’s free energy and derive the magnetization, susceptibility, internal energy, and specific heat. These results are compared with numerical simulations performed with the BKL algorithm. We find that the approximate expressions and numerical simulations agree in regions where the approximation is valid.
Author: Mathieu Gaudreault
Institutions: The University of Melbourne, Peter MacCallum Cancer Centre
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
OpenAlex ID: W4409452063