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Disappearance of the de Almeida-Thouless line in six dimensions

M. A. Moore, A. J. Bray
2011 Physical Review B  

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2011 pre-print arXiv:1102.1675v2 fatcat:pfvnegpw7fcjlihn4f4culxyhe

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2011 accepted
arXiv:1102.1675v3 fatcat:gkogjhrejbgpnod7vnrmqpybja
2011 pre-print
arXiv:1102.1675v1 fatcat:6gzm7ho5lvebxdpcm57i2smu6u
We show that the Almeida-Thouless line in Ising spin glasses vanishes when their dimension d -> 6 as h_AT^2/T_c^2 = C(d-6)^4(1- T/T_c)^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.
doi:10.1103/physrevb.83.224408 fatcat:fb6xep4y2rcdlpn4f4v423qh3e
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M. A. Moore, A. J. Bray. "Disappearance of the de Almeida-Thouless line in six dimensions." Physical Review B 83.22 (2011)