One-step replica-symmetry-breaking phase below the de Almeida-Thouless line in low-dimensional spin glasses

Abstract

The de Almeida-Thouless (AT) line is the phase boundary in the temperature--magnetic field plane of an Ising spin glass at which a continuous (i.e. second-order) transition from a paramagnet to a replica-symmetry-breaking (RSB) phase occurs, according to mean-field theory. Here, using field-theoretic perturbative renormalization group methods on the Bray-Roberts reduced Landau-Ginzburg-type theory for a short-range Ising spin glass in space of dimension $d$, we show that at nonzero magnetic field the nature of the corresponding transition is modified as follows: a) for $d-6$ small and positive, with increasing field on the AT line first, the ordered phase just below the transition becomes the so-called one-step RSB, instead of the full RSB that occurs in mean-field theory; the transition on the AT line remains continuous with a diverging correlation length. Then at a higher field, a tricritical point separates the latter transition from a quasi-first-order one, that is one at which the correlation length does not diverge, and there is a jump in part of the order parameter, but no latent heat. The location of the tricritical point tends to zero as $d\to 6^{+}$; b) for $d\le 6$, we argue that the quasi-first-order transition could persist down to arbitrarily small nonzero fields, with a transition to full RSB still expected at lower temperature. Whenever the quasi-first-order transition occurs, it is at a higher temperature than the AT transition would be for the same field, preempting it as the temperature is lowered. We also draw attention to the similarity of the "dynamically-frozen" state, which occurs at temperatures just above the quasi-first-order transition, and the "metastate-average state" of the one-step RSB phase, and discuss the issue of the number of pure states in either.

arXiv comment17 pages, 2 figures. v2: minor changes and corrections, new Appendix, added references; 20 pages. v3: published version. v4: typo fixed in eq. (2.5)

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• Spin-glass dynamics: experiment, theory and simulation
• Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field
• Spin glasses in a field show a phase transition varying the distance among real replicas (and how to exploit it to find the critical line in a field)
• Critical exponents of the spin glass transition in a field at zero temperature
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Evidence of de Almeida-Thouless line below six dimensions
• Long-range spin glass in a field at zero temperature
• Replica Symmetry Broken States of some Glass Models