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Lattice models are useful for understanding behaviors of interacting complexmany-body systems. The lattice dimer model has been proposed to study theadsorption of diatomic molecules on a substrate. Here we analyze the partitionfunction of the dimer model on an $2 M \times 2 N$ checkerboard lattice wrappedon a torus and derive the exact asymptotic expansion of the logarithm of thepartition function. We find that the internal energy at the critical point isequal to zero. We also derive the exact finite-size corrections for the freeenergy, the internal energy, and the specific heat. Using the exact partitionfunction and finite-size corrections for the dimer model on finite checkerboardlattice we obtain finite-size scaling functions for the free energy, theinternal energy, and the specific heat of the dimer model. We investigate theproperties of the specific heat near the critical point and find thatspecific-heat pseudocritical point coincides with the critical point of thethermodynamic limit, which means that the specific-heat shift exponent$\lambda$ is equal to $\infty$. We have also considered the limit $N \to\infty$ for which we obtain the expansion of the free energy for the dimermodel on the infinitely long cylinder. From a finite-size analysis we havefound that two conformal field theories with the central charges $c = 1$ forthe height function description and $c = -2$ for the construction using amapping of spanning trees can be used to describe the dimer model on thecheckerboard lattice.

Finite-size corrections and scaling for the dimer model on the checkerboard lattice