Finite size and boundary effects in critical two-dimensional free-fermion models

Here we will consider the finite-size scaling, finite-size corrections and boundary effects for the critical two-dimensional free-fermion models. A short review of significant achievements and possibilities is given. However, this review is still far from completeness. We derive the exact finite-size corrections for the set of free models of statistical mechanics, including Ising model, dimer model, resistor network and spanning tree model under different boundary conditions. We have shown that the partition functions of all these models can be written in terms of the only object, namely, the partition function with twisted boundary conditions.