Triangular Ising antiferromagnet through a fermionic lens, part 2: information-theoretic aspects of zero-temperature states on cylinders

TL;DR

This paper investigates the zero-temperature states of the triangular lattice Ising antiferromagnet on cylindrical geometries using a fermionic representation, revealing how mutual information decay depends on cylinder circumference and boundary conditions.

Contribution

It introduces a fermionic approach to analyze mutual information in TIAFM systems, clarifying previously puzzling decay behaviors and their dependence on geometric and boundary factors.

Findings

Mutual information decay rate varies smoothly with cylinder circumference.

End-to-end mutual information depends on circumference residue class mod 3.

Decay can be as slow as inverse square of cylinder length.

Abstract

A classical lattice spin model wrapped on a cylinder is profitably viewed as a chain of rings of spins. From that perspective, mutual information between ring configurations plays much the same role as spin-spin correlation functions in simpler settings. We study zero-temperature states of triangular lattice Ising antiferromagnet (TIAFM) systems from this point of view using a fermionic representation presented in a companion paper (Part 1). On infinite cylinders, ring-to-ring mutual information falls off asymptotically at a rate which decreases smoothly with cylinder circumference, but the end-to-end mutual information for finite cylinders depends strongly on the residue class modulo 3 of the circumference as well as on whether spin periodicity or antiperiodicity is imposed in the circumferential direction. In some cases, the falloff is only as the inverse square of the cylinder length. These features, puzzling within the original spin formulation, are easily understood and calculated within the fermionic formulation.