Corrections to finite--size scaling in the phi^4 model on square lattices

Understand

Corrections to scaling in the two-dimensional scalar phi^4 model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L (from 4 to 1536) and different values of the phi^4 coupling constant lambda, i.~e., lambda = 0.1, 1, 10.

• According to our analysis, amplitudes of the nontrivial correction terms with the correction-to-scaling exponents omega_l < 1 become small when approaching the Ising limit (lambda --> infinity), but such corrections generally exist in the 2D phi^4 model.
• Analytical arguments show the existence of corrections with the exponent 3/4.
• The numerical analysis suggests that there exist also corrections with the exponent 1/2 and, very likely, also corrections with the exponent about 1/4, which are detectable at lambda = 0.1.