Universality and the five-dimensional Ising model

We solve the long-standing discrepancy between Monte Carlo results and the renormalization prediction for the Binder cumulant of the five-dimensional Ising model. Our conclusions are based on accurate Monte Carlo data for systems with linear sizes up to L=22. A detailed analysis of the corrections to scaling allows the extrapolation of these results to L=\infinity. Our determination of the critical point, K_c=0.1139150 (4), is more than an order of magnitude more accurate than previous estimates.Comment: 6 pages LaTeX, 1 PostScript figure. Uses cite.sty (included) and epsf.sty. Also available as PostScript and PDF file at http://www.tn.tudelft.nl/tn/erikpubs.htm

Finite-size Scaling and Universality above the Upper Critical Dimensionality

According to renormalization theory, Ising systems above their upper critical dimensionality d_u = 4 have classical critical behavior and the ratio of magnetization moments Q = ^2 / has the universal value 0.456947... However, Monte Carlo simulations of d = 5 Ising models have been reported which yield strikingly different results, suggesting that the renormalization scenario is incorrect. We investigate this issue by simulation of a more general model in which d_u < 4, and a careful analysis of the corrections to scaling. Our results are in a perfect agreement with the renormalization theory and provide an explanation of the discrepancy mentioned.Comment: 5 pages RevTeX, 1 PostScript figure. Accepted for publication in Physical Review Letter