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The free energy of the square lattice Ising model with interactions alternating in horizontal and vertical directions

  • Kazuhiko Minami
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Abstract

The free energy of the Ising model on the square lattice with alternating interactions in both horizontal and vertical directions is exactly derived. This model is distinct from the checkerboard Ising model. The result includes Onsager's free energy as a special case, and also includes Lee-Yang's free energy with an imaginary field, and relates these two solutions via continuous parameters. The result includes a generalization of Lee-Yang's result to cases with four different couplings. It is also derived that each imaginary magnetic field iπ/2 applied to a lattice site corresponds to a single frustrated square in its dual lattice.

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Cite

BibTeXRIS
BibTeX
@misc{minami2026free,
  title = {{The free energy of the square lattice Ising model with interactions alternating in horizontal and vertical directions}},
  author = {Kazuhiko Minami},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.16225},
  eprint = {2606.16225},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.16225},
}
RIS
TY  - UNPB
TI  - The free energy of the square lattice Ising model with interactions alternating in horizontal and vertical directions
AU  - Kazuhiko Minami
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2606.16225
UR  - https://arxiv.org/abs/2606.16225
AB  - The free energy of the Ising model on the square lattice with alternating interactions in both horizontal and vertical directions is exactly derived. This model is distinct from the checkerboard Ising model. The result includes Onsager's free energy as a special case, and also includes Lee-Yang's free energy with an imaginary field, and relates these two solutions via continuous parameters. The result includes a generalization of Lee-Yang's result to cases with four different couplings. It is also derived that each imaginary magnetic field iπ/2 applied to a lattice site corresponds to a single frustrated square in its dual lattice.
ER  -