Series and Monte Carlo study of high-dimensional Ising models

Misha Gofman*, Joan Adler, Amnon Aharony, A. B. Harris, Dietrich Stauffer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Ising models in high dimensions are used to compare high-temperature series expansions with Monte Carlo simulations. Simulations of the magnetization on four-, six-, and seven-dimensional hypercubic lattices give consistent values of the critical temperature from both equilibrium and nonequilibrium data for d=6 and 7. We tabulate 15 terms of series expansions for the susceptibility for general d and give J/kBTc=0.092295 (3) and 0.077706 (2) for d=6 and 7. In contrast to five dimensions, where earlier series found nonanalytic scaling corrections, for d=6 and 7 the leading scaling correction may be analytic in T-Tc. In most cases these expansions gave more accurate results than these simulations.

Original languageEnglish
Pages (from-to)1221-1230
Number of pages10
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Jun 1993


  • Ising models
  • Monte Carlo simulation
  • Series expansions
  • corrections to scaling


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