Universal amplitude ratios for scaling corrections on Ising strips

Exact finite-size corrections for the spanning-tree model under different boundary conditions

We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions in terms of a principal partition function with twisted-boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the logarithm of the partition function for each case. We have also established several groups of identities relating spanning-tree partition functions for the different boundary conditions. We also explain an apparent discrepancy between logarithmic correction terms in the free energy for a two-dimensional spanning-tree model with periodic and free-boundary conditions and conformal field theory predictions. We have obtained corner free energy for the spanning tree under free-boundary conditions in full agreement with conformal field theory predictions.

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.