  We have tested the leading correction-to-scaling exponent omega in
O(n)-symmetric models on a three-dimensional lattice by analysing the recent
Monte Carlo (MC) data. We have found that the effective critical exponent,
estimated at finite sizes of the system L and L/2, decreases remarkably within
the range of the simulated L values. This shows the incorrectness of some
claims that omega has a very accurate value 0.845(10) at n=1. A selfconsistent
infinite volume extrapolation yields row estimates omega=0.547, omega=0.573,
and omega=0.625 at n=1, 2, and 3, respectively, in approximate agreement with
the corresponding exact values 1/2, 5/9, and 3/5 predicted by our recently
developed GFD (grouping of Feynman diagrams) theory. We have fitted the MC data
for the susceptibility of 3D Ising model at criticality showing that the
effective critical exponent eta tends to increase well above the usually
accepted values around 0.036. We have fitted the data within [L;8L], including
several terms in the asymptotic expansion with fixed exponents, to obtain the
effective amplitudes depending on L. This method clearly demonstrates that the
critical exponents of GFD theory are correct (the amplitudes converge to
certain asymptotic values at L tending to infinity), whereas those of the
perturbative renormalization group (RG) theory are incorrect (the amplitudes
diverge). A modification of the standard Ising model by introducing suitable
"improved" action (Hamiltonian) does not solve the problem in favour of the
perturbative RG theory.
