Logarithmic Conformal Field Theory and Boundary Effects in the Dimer Model

We study the finite-size corrections of the dimer model on $\infty \times N$ square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections in a crucial way depend on the parity of $N$; we also show that such unusual finite-size behavior can be fully explained in the framework of the $c=-2$ logarithmic conformal field theory.