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 inverse
correlation length of the critical two-dimensional Ising model. They obtained
the universal amplitude ratio for the coefficients of two series. In this study
we give a simple derivation of this universal relation; we do not use an
explicit form of series expansion. Moreover, we show that the Izmailian 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 temperature and has the
same form as the finite-size scaling.Comment: 4 pages, RevTeX, to appear in Phys. Rev. E, Rapid Communication
