Corrections to finite-size scaling in the $\varphi^4$ model on square lattices

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