Disappearance of the de Almeida-Thouless line in six dimensions
Abstract
We show that the Almeida-Thouless line in Ising spin glasses vanishes when their dimension d -> 6 as hAT2/Tc2 = C(d-6)4(1- T/Tc)d/2 - 1, where C is a constant of order unity. An equivalent result which could be checked by simulations is given for the one-dimensional Ising spin glass with long-range interactions. It is shown that replica symmetry breaking also stops as d -> 6.
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