  We study a low temperature anisotropic anti-ferromagnetic 2D Ising model
through the guise of a certain dimer model. This model has a bijection with a
one-dimensional particle system equipped with creation and annihilation. In the
thermodynamic limit, we determine the explicit phase diagrams as functions of
temperature and anisotropy. Two values of the anisotropy are of particular
interest - the 'critical' value and the 'independent' value. At independence,
the particle system has the same distribution as the two colored noisy voter
model. Its limiting measure under a natural scaling window is the Continuum
Noisy Voter Model. At criticality, the distribution of particles on a given
horizontal line, is a Pfaffian point process whose kernel in the scaling window
can be written explicitly in terms of Bessel functions.
