SciPost logo

Anisotropic scaling of the two-dimensional Ising model I: the torus

Hendrik Hobrecht, Alfred Hucht

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.

Cited by 9

Crossref Cited-by

Ontology / Topics

See full Ontology or Topics database.

Ising model Two-dimensional systems

Authors / Affiliation: mappings to Contributors and Organizations

See all Organizations.
Funder for the research work leading to this publication