Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional ising model

E. Luijten*, K. Binder, H. W J Blöte

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

63 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)289-297
Number of pages9
JournalEuropean Physical Journal B
Volume9
Issue number2
DOIs
StatePublished - May 2 1999

Keywords

  • 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

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