Comparison between finite-size field theory and Monte Carlo simulations for the three-dimensional Ising model

Recent field-theoretic predictions of finite-size effects for various thermodynamic quantities near the critical point are compared with new accurate Monte Carlo (MC) data for the L × L × L Ising model obtained from a cluster-algorithm special-purpose computer. Owing to the large size (L = 32, 64, 128, 256) of the Ising models, these MC data permit to test the finite-size field theory in the asymptotic scaling region above and below Tc. The results constitute the most accurate confirmation of finite-size scaling in three dimensions obtained to date in a wide range of temperatures. Agreement with the predicted shape of the finite-size scaling functions is found on a quantitative level.