  I propose a fixed-range interaction multicomponent spin model, to be used as
a physical analog to problems in plane geometry. Specifically, the model is
applied to the open problem of the chromatic number of the plane. When spin
values are interpreted as colors, the lowest energy configurations of the
lattice spin system can be interpreted as approximations to plane colorings. In
general minimum energy configurations of the model give optimal colorings,
corresponding to minimum probability of any color realizing distance one.
Approximate optimal lattice colorings with two to seven colors towards the
continuum limit suggest that a true coloring of the plane cannot be achieved
with less than seven colors.
