Corrections to scaling in the 2D phi^4 model: Monte Carlo results and some related problems

Monte Carlo (MC) simulations have been performed for a refined estimation of the correction-to-scaling exponent omega in the 2D phi^4 model. The best estimate omega=1.546(30) has been obtained from the finite-size scaling of the susceptibility data in the range of linear lattice sizes L from 128 to 2048 at the critical value of the Binder cumulant, this result is confirmed also by several other MC estimations. It served as a basis for a critical reconsideration of some earlier theoretical conjectures and scaling assumptions. In particular, we have corrected and refined our previous analysis by grouping Feynman diagrams. The renewed analysis gives omega = 4-d-2 eta as some approximation for spatial dimensions d<4, or omega approximately 1.5 in two dimensions. Our MC value is comparable with the known results of the epsilon-expansion.