Universal relations in the finite-size correction terms of two-dimensionalIsing models - art. no. 035103

Quite recently, Izmailian and Hu [Phys. Rev. Lett. 86, 5160 (2001)] studied the finite-size correction terms for the free energy per spin and the inve rse correlation length of the critical two-dimensional Ising model. They ob tained the universal amplitude ratio for the coefficients of two series. Tn this study we give a simple derivation of this universal relation; we do n ot use an explicit form of series expansion. Moreover, we show that the Izm ailian and Hu's relation is reduced to a simple and exact relation between the free energy and the correlation length. This equation holds at any temp erature and has the same form as the finite-size scaling.