Classical triangular lattice antiferromagnetic Ising model as a free-fermion/superconductor system

TL;DR

This paper maps the classical triangular lattice antiferromagnetic Ising model to a free-fermion/superconductor system, providing a new analytical approach to study its thermodynamics and zero-temperature states.

Contribution

It introduces a fermionic representation of the TAFIM as a reduced BCS model, enabling exact zero-temperature analysis and approximate finite-temperature thermodynamics.

Findings

Exact fermionic representation at zero temperature.

Approximate thermodynamic functions at nonzero temperature.

Identification of a continuum of zero-temperature macrostates.

Abstract

We present a treatment of the triangular lattice antiferromagnetic Ising model (TAFIM) based on a small number of elementary ideas common to statistical and solid-state physics. The TAFIM is represented as a reduced BCS model in one space, one (imaginary) time dimension. The representation is approximate for nonzero temperature, but allows quick derivation of asymptotically exact thermodynamic functions, and the divergence of the spin-spin correlation length. The fermionic representation is exact at zero temperature. We demonstrate the existence of a two-dimensional continuum of zero-temperature equilibrium macrostates characterized by satisfied bond fractions of the three different orientations, and calculate their entropy densities.