Amplitude ratios for critical systems in the c=-2 universality class.

We study the finite-size corrections of the critical dense polymer (CDP) and the dimer models on ∞×N rectangular lattice. We find that the finite-size corrections in the CDP and dimer models depend in a crucial way on the parity of N, and a change of the parity of N is equivalent to the change of boundary conditions. We present a set of universal amplitude ratios for amplitudes in finite-size correction terms of critical systems in the universality class with central charge c=-2. The results are in perfect agreement with a perturbated conformal field theory under the assumption that all analytical corrections coming from the operators which belongs to the tower of the identity. Our results inspire many interesting problems for further studies.