https://doi.org/10.1007/s100510050768
Finite-size scaling above the upper critical dimension revisited: the case of the five-dimensional Ising model
1
Max-Planck-Institut für Polymerforschung, Postfach 3148, 55021 Mainz, Germany
2
Institut für Physik, WA 331, Johannes Gutenberg-Universität, 55099 Mainz, Germany
3
Department of Physics, Delft University of Technology, P.O. Box 5046, 2600 GA Delft,
The Netherlands
Received:
4
September
1998
Published online: 15 May 1999
Monte-Carlo results for the moments of the magnetization
distribution of the nearest-neighbor Ising ferromagnet in a Ld geometry,
where L (
) is the linear dimension of a hypercubic lattice
with periodic boundary conditions in d=5 dimensions, are analyzed in the
critical region and compared to a recent theory of Chen and Dohm (CD) [X.S.
Chen and V. Dohm, Int. J. Mod. Phys. C 9, 1007 (1998)]. We show that this
finite-size scaling theory (formulated in terms of two scaling variables) can
account for the longstanding discrepancies between Monte-Carlo results and the
so-called "lowest-mode" theory, which uses a single scaling variable
where
is the temperature distance from the
critical temperature, only to a very limited extent. While the CD theory gives
a somewhat improved description of corrections to the "lowest-mode" results
(to which the CD theory can easily be reduced in the limit
,
,
fixed) for the fourth-order cumulant, discrepancies are
found for the susceptibility (
). Reasons for these
problems are briefly discussed.
PACS: 05.70.Jk – Critical point phenomena / 64.60.-i – General studies of phase transitions / 75.40.Mg – Numerical simulation studies
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999