Exact finite-size scaling with corrections in the two-dimensional Ising model with special boundary conditions

TL;DR

This paper provides an exact analysis of finite-size scaling and corrections in the 2D Ising model with special boundary conditions, revealing detailed behavior of Fisher zeroes and specific heat at criticality.

Contribution

It offers the first exact determination of finite-size scaling and correction terms for the 2D Ising model with Brascamp-Kunz boundary conditions.

Findings

Exact finite-size scaling behavior of Fisher zeroes determined.

Analytic corrections to scaling found, shift exponent differs from 1/nu.

Results applicable to understanding critical phenomena in finite systems.

Abstract

The two-dimensional Ising model with Brascamp-Kunz boundary conditions has a partition function more amenable to analysis than its counterpart on a torus. This fact is exploited to exactly determine the full finite-size scaling behaviour of the Fisher zeroes of the model. Moreover, exact results are also determined for the scaling of the specific heat at criticality, for the specific-heat peak and for the pseudocritical points. All corrections to scaling are found to be analytic and the shift exponent $\lambda$ does not coincide with the inverse of the correlation length exponent $1/\nu$.