  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.
