Communicating through a geometrically frustrated channel

TL;DR

This paper models the zero-temperature triangular lattice Ising antiferromagnet as noninteracting fermions on a ring, revealing boundary influence, multiple phases, and communication capabilities even with negligible spin correlations, and discusses phase changes at positive temperature.

Contribution

It introduces a fermionic formulation of the TIAFM on a cylinder, elucidating boundary effects, phase behavior, and information transmission properties at zero temperature.

Findings

Boundary conditions influence bulk entropy density.

Multiple pure phases with different entropy densities exist.

Boundary conditions enable communication despite vanishing spin correlations.

Abstract

We propose an intuitively appealing formulation of the zero-temperature triangular lattice Ising antiferromagnet (TIAFM) on a cylinder as a model of noninteracting fermions hopping on a ring and evolving in imaginary time with pair annihilation events. Among the features of the model which can then be related to local semi-conservation of particle number are: infinite-range influence of boundary conditions, multiple "zero temperature pure phases" in the infinite-length limit differing in entropy density, sensitivity of the asymptotic rate of decay (with respect to length) of mutual information between end configurations to circumference modulo 3, and even the known power-law falloff of the spin-spin correlator on an infinite plane. The ability of boundary conditions to determine the bulk entropy density enables communication between the two far-separated ends of such a cylinder even when all pair-wise spin-spin correlations between the ends are vanishingly small. In the fermionic language, breakdown of these zero-temperature phenomena at positive temperature is understood as passage of the system into a superconducting phase.