  We study a model of close-packed dimers on the square lattice with a nearest
neighbor interaction between parallel dimers. This model corresponds to the
classical limit of quantum dimer models [D.S. Rokhsar and S.A. Kivelson, Phys.
Rev. Lett.{\bf 61}, 2376 (1988)]. By means of Monte Carlo and Transfer Matrix
calculations, we show that this system undergoes a Kosterlitz-Thouless
transition separating a low temperature ordered phase where dimers are aligned
in columns from a high temperature critical phase with continuously varying
exponents. This is understood by constructing the corresponding Coulomb gas,
whose coupling constant is computed numerically. We also discuss doped models
and implications on the finite-temperature phase diagram of quantum dimer
models.
