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

摘要

Corrections to scaling in the 3D Ising model are studied based on nonperturbative 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 approximate to 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 <= 2560 yields omega = 0.21(29), in agreement with this statement. We reconsider the MC estimation of ! from smaller lattice sizes, L <= 384, using different finite-size scaling methods, and show that these sizes are still too small, since no convergence to the same result is observed. In particular, estimates ranging from omega = 0.866(21) to omega = 1.247(73) are obtained, using MC data for thermodynamic average quantities, as well as for partition function zeros. However, a trend toward smaller omega values is observed in one of these cases in a refined estimation from extended data up to L = 1536. We discuss the influence of omega on the estimation of critical exponents eta and nu.