  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.
