2 research outputs found
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