1202.1188 (Mihai Ciucu)

The interaction of collinear gaps of arbitrary charge in a two
dimensional dimer system    [PDF]

Mihai Ciucu

The correlation of gaps in dimer systems was introduced in 1963 by Fisher and
Stephenson, who looked at the interaction of two monomers generated by the
rigid exclusion of dimers on the closely packed square lattice. In previous
work we considered the analogous problem on the hexagonal lattice, and we
extended the set-up to include the correlation of any finite number of monomer
clusters. For fairly general classes of monomer clusters we proved that the
asymptotics of their correlation is given, for large separations between the
clusters, by a multiplicative version of Coulomb's law for 2D electrostatics.
However, our previous results required that the monomer clusters consist (with
possibly one exception) of an even number of monomers. In this paper we
determine the asymptotics of general defect clusters along a lattice diagonal
in the square lattice (involving an arbitrary, even or odd number of monomers),
and find that it is given by the same Coulomb law. We also obtain a conceptual
interpretation for the multiplicative constant as the product of the
correlations of the individual clusters.

View original: http://arxiv.org/abs/1202.1188