Contours of constant χsG in the H-T plane: Mean-field versus droplet theories of Ising spin glasses

Rajiv R.P. Singh, David A. Huse

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8 Scopus citations


One of the central features of the mean-field theory of Ising spin glasses is the de Almeida-Thouless phase transition line in the H-T plane, where the spin-glass susceptibility χSG diverges. Contours of constant χSG in the paramagnetic phase go to high fields as T→0 in mean-field theory. In contrast, in the droplet theory for short-ranged spin glasses, χSG remains finite in a field and the contours go to H=0 as T→0. We have investigated the constant χSG contours both in the SK model and for d-dimensional short-ranged spin glasses. For the latter we use transfer matrix methods in d=1 and high-temperature expansions and Monte Carlo simulations in higher d. The results are in good accord with droplet theory for d=1 and 2. For d=3 the evidence remains ambiguous, although extrapolations of high-temperature series are qualitatively different from d=2.

Original languageEnglish (US)
Pages (from-to)5225-5227
Number of pages3
JournalJournal of Applied Physics
Issue number8
StatePublished - Dec 1 1991
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


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