Monte-Carlo results for the moments 〈Mk〉 of the magnetization distribution of the nearest-neighbor Ising ferromagnet in a Ld geometry, where L (4 ≤ L ≤ 22) 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 tLd/2 where t = T/Tc - 1 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 t → 0, L → ∞, tLd/2 fixed) for the fourth-order cumulant, discrepancies are found for the susceptibility (Ld〈M2〉). Reasons for these problems are briefly discussed.
- 05.70.Jk Critical point phenomena
- 64.60.-i General studies of phase transitions
- 75.40.Mg Numerical simulation studies
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics