 1049 Paul Federbush
 Tilings With Very Elastic Dimers
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Mar 15, 10

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Abstract. We consider tiles (dimers) each of which covers two vertices of a rectangular
lattice. There is a normalized translation invariant weighting on the shape
of the tiles. We study the pressure, p, or entropy, (one over the volume
times the logarithm of the partition function). We let p_0 (easy to
compute) be the pressure in the limit of absolute smoothness (the weighting
function is constant). We prove that as the smoothness of the weighting
function, suitably defined, increases, p converges to p_0, uniformly in
the volume. It is the uniformity statement that makes the result
nontrivial. In an earlier paper the author proved this, but with an
additional requirement of a certain falloff on the weighting function.
Herein falloff is not demanded, but there is the technical requirement
that each dimer connect a black vertex with a white vertex, vertices colored
as on a checker board. This seems like a very basic result in the theory
of pressure (entropy) of tilings.
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