Approximate thermodynamics of the two-dimensional Ising model in an external magnetic field
- Author(s)
- Gaudreault, M;
- Details
- Publication Year 2025-05,Volume 58,Issue #18,Page 185001
- Journal Title
- Journal of Physics A: Mathematical and Theoretical
- Publication Type
- Research 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.
- Publisher
- IOP Publishing
- Keywords
- two-dimensional Ising model; external field; thermodynamics; magnetization; susceptibility
- Department(s)
- Physical Sciences
- Publisher's Version
- https://doi.org/10.1088/1751-8121/adcd32
- Open Access at Publisher's Site
https://doi.org/10.1088/1751-8121/adcd32- Terms of Use/Rights Notice
- Refer to copyright notice on published article.
Creation Date: 2026-01-09 05:37:26
Last Modified: 2026-01-09 05:38:15