We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings, as well as for the corresponding universal free energy finite-size scaling functions. Therefore, we review the dimer mapping, as well as the interplay between its topology and the different types of boundary conditions. As a central result, we show how both the finite system as well as the scaling form decay into contributions for the bulk, a characteristic finite-size part, and - if present - the surface tension, which emerges due to at least one antiperiodic boundary in the system. For the scaling limit we extend the proper finite-size scaling theory to the anisotropic case and show how this anisotropy can be absorbed into suitable scaling variables.
Cited by 4
Dohm et al., Multiparameter universality and conformal field theory for anisotropic confined systems: test by Monte Carlo simulations
J. Phys. A: Math. Theor. 54, 23LT01 (2021) [Crossref]
Dohm et al., Exact Critical Casimir Amplitude of Anisotropic Systems from Conformal Field Theory and Self-Similarity of Finite-Size Scaling Functions in
Phys. Rev. Lett. 126, 060601 (2021) [Crossref]
Hobrecht et al., Anisotropic scaling of the two-dimensional Ising model II: surfaces and boundary fields
SciPost Phys. 8, 032 (2020) [Crossref]
Hucht, The square lattice Ising model on the rectangle III: Hankel and Toeplitz determinants
J. Phys. A: Math. Theor. 54, 375201 (2021) [Crossref]
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- 1 Hendrik Hobrecht,
- 1 Fred Hucht