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Evidence that the AT transition disappears below six dimensions (2402.03711v5)

Published 6 Feb 2024 in cond-mat.dis-nn and cond-mat.stat-mech

Abstract: One of the key predictions of Parisi's broken replica symmetry theory of spin glasses is the existence of a phase transition in an applied field to a state with broken replica symmetry. This transition takes place at the de Almeida-Thouless (AT) line in the $h-T$ plane. We have studied this line in the power-law diluted Heisenberg spin glass in which the probability that two spins separated by a distance $r$ interact with each other falls as $1/r{2\sigma}$. In the presence of a random vector-field of variance $h_r2$ the phase transition is in the universality class of the Ising spin glass in a field. Tuning $\sigma$ is equivalent to changing the dimension $d$ of the short-range system, with the relation being $d =2/(2\sigma -1)$ for $\sigma < 2/3$. We have found by numerical simulations that $h_{\text{AT}}2 \sim (2/3 -\sigma)$ implying that the AT line does not exist below $6$ dimensions and that the Parisi scheme is not appropriate for spin glasses in three dimensions.

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