  The corrections to finite-size scaling in the critical two-point correlation
function G(r) of 2D Ising model on a square lattice have been studied
numerically by means of exact transfer-matrix algorithms. The systems of square
geometry with periodic boundaries oriented either along <10> or along <11>
direction have been considered, including up to 800 spins. The calculation of
G(r) at a distance r equal to the half of the system size L shows the existence
of an amplitude correction proportional to 1/L^2. A nontrivial correction
proportional to 1/L^0.25 of a very small magnitude also has been detected in
agreement with predictions of our recently developed GFD (grouping of Feynman
diagrams) theory. A refined analysis of the recent MC data for 3D Ising, phi^4,
and XY lattice models has been performed. It includes an analysis of the
partition function zeros of 3D Ising model, an estimation of the
correction-to-scaling exponent omega from the Binder cumulant data near
criticality, as well as a study of the effective critical exponent eta and the
effective amplitudes in the asymptotic expansion of susceptibility at the
critical point. In all cases a refined analysis is consistent with our (GFD)
asymptotic values of the critical exponents (nu=2/3, omega=1/2, eta=1/8 for 3D
Ising model and omega=5/9 for 3D XY model), while the actually accepted
"conventional" exponents are, in fact, effective exponents which are valid for
approximation of the finite--size scaling behavior of not too large systems.
