Corrections to finite-size scaling in the φ4 model on square lattices

Abstract

Corrections to scaling in the two-dimensional (2D) scalar [Formula: see text] model are studied based on nonperturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L ([Formula: see text]) and different values of the [Formula: see text] coupling constant [Formula: see text], i.e. [Formula: see text], 1, 10. According to our analysis, amplitudes of the nontrivial correction terms with the correction–to–scaling exponents [Formula: see text] become small when approaching the Ising limit ([Formula: see text]), but such corrections generally exist in the 2D [Formula: see text] model. Analytical arguments show the existence of corrections with the exponent [Formula: see text]. The numerical analysis suggests that there exist also corrections with the exponent [Formula: see text] and, perhaps, also with the exponent about [Formula: see text], which are detectable at [Formula: see text]. The numerical tests provide an evidence that the structure of corrections to scaling in the 2D [Formula: see text] model differs from the usually expected one in the 2D Ising model.