We study the classical hard-core dimer model on the triangular lattice.
Following Kasteleyn's fundamental theorem on planar graphs, this problem is
soluble by Pfaffians. This model is particularly interesting for, unlike the
dimer problems on the bipartite square and hexagonal lattices, its correlations
are short ranged with a correlation length of less than one lattice constant.
We compute the dimer-dimer and monomer-monomer correlators, and find that the
model is deconfining: the monomer-monomer correlator falls off exponentially to
a constant value sin(pi/12)/sqrt(3) = .1494..., only slightly below the
nearest-neighbor value of 1/6. We also consider the anisotropic triangular
lattice model in which the square lattice is perturbed by diagonal bonds of one
orientation and small fugacity. We show that the model becomes non-critical
immediately and that this perturbation is equivalent to adding a mass term to
each of two Majorana fermions that are present in the long wavelength limit of
the square-lattice problem.Comment: 15 pages, 5 figures. v2: includes analytic value of monomer-monomer
correlator, changes titl
