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Corrections to scaling in the two–dimensional scalar ϕ 4 model are studied based on non–perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L (4 ≤ L ≤ 1536) and different values of the ϕ 4 coupling constant λ, i. e., λ = 0.1,1,10. According to our analysis, amplitudes of the nontrivial correction terms with the correction–to–scaling exponents ωl < 1 become small when approaching the Ising limit (λ → ∞), but such corrections generally exist in the 2D ϕ 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 λ = 0.1. The numerical tests clearly show that the structure of corrections to scaling in the 2D ϕ 4 model differs from the usually expected one in the 2D Ising model.

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