Monte Carlo test of critical exponents and amplitudes in 3D Ising and phi⁴ lattice models

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.