SciPost Phys. 7, 026 (2019) ·
published 2 September 2019

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We present detailed calculations for the partition function and the free
energy of the finite twodimensional 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 finitesize
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 finitesize 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
finitesize scaling theory to the anisotropic case and show how this anisotropy
can be absorbed into suitable scaling variables.
Submissions
Submissions for which this Contributor is identified as an author:
Dr Hucht: "We thank Prof. Perk for his de..."
in Report on Anisotropic scaling of the twodimensional Ising model I: The torus