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

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Abstract
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.