Exact finite-size corrections in the dimer model on a planar square lattice

We consider the dimer model on the rectangular ##IMG##
[http://ej.iop.org/images/1751-8121/52/33/335001/aab2fedieqn001.gif] lattice with free boundary
conditions. We derive exact expressions for the coefficients in the asymptotic expansion of the free
energy in terms of the elliptic theta functions ( ##IMG##
[http://ej.iop.org/images/1751-8121/52/33/335001/aab2fedieqn002.gif] ) and the elliptic integral of
second kind ( E ), up to 22nd order. Surprisingly we find that ratio of the coefficients f   p   in
the free energy expansion for strip ( ##IMG##
[http://ej.iop.org/images/1751-8121/52/33/335001/aab2fedieqn003.gif] ) and square ( ##IMG##
[http://ej.iop.org/images/1751-8121/52/33/335001/aab2fedieqn004.gif] ) geometries ##IMG##
[http://ej.iop.org/images/1751-8121/52/33/335001/aab2fedieqn005.gif] in the limit of large p   tends
t...

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