Jevgenijs Kaupužs

Corrections to finite-size scaling in the 3D Ising model based on nonperturbative approaches and Monte Carlo simulations

Corrections to scaling in the 3D Ising model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L. Analytical arguments show the existence of corrections with the exponent (gamma-1)/nu (approximately 0.38), the leading correction-to-scaling exponent being omega =< (gamma-1)/nu. A numerical estimation of omega from the susceptibility data within 40 =< L =< 2048 yields omega=0.25(33). It is consistent with the statement omega =< (gamma-1)/nu, as well as with the value omega = 1/8 of the GFD theory. We reconsider the MC estimation of omega from smaller lattice sizes to show that it does not lead to conclusive results, since the obtained values of omega depend on the particular method chosen. In particular, estimates ranging from omega =1.274(72) to omega=0.18(37) are obtained by four different finite-size scaling methods, using MC data for thermodynamic average quantities, as well as for partition function zeros. We discuss the influence of omega on the estimation of exponents eta and nu.

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

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.