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