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arXiv:cond-mat/9812401 · Physical Review Letters

Comment on “Ising Spin Glasses in a Magnetic Field”

Enzo Marinari, Giorgio Parisi A, Francesco Zuliani

Published Jan 31, 2000• 16 citations
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Abstract

In ref. cond-mat/9811419 Houdayer and Martin analyze the T=0 3d EA spin glass with a magnetic field $B$. By using a new, powerful method, they determine an effective critical field $B_c$ as a function of the lattice size $L$. They use their results to deduce that the model is behaving like in the droplet approach and not like the mean-field theory. We show here, by using some unpublished data, that this very interesting method and numerical results are completely compatible with the behavior implied by the Replica Symmetry Breaking theory.

DOI
10.1103/physrevlett.84.1056

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In ref. cond-mat/9811419 Houdayer and Martin analyze the T=0 3d EA spin glass with a magnetic field BBB. By using a new, powerful method, they determine an effective critical field BcB_cBc​ as a function of the lattice size LLL. They use their results to deduce that the model is behaving like in the droplet approach and not like the mean-field theory. We show here, by using some unpublished data, that this very interesting method and numerical results are completely compatible with the behavior implied by the Replica Symmetry Breaking theory.
A recent interesting paper [Yucesoy et al. Phys. Rev. Lett. 109, 177204 (2012), arXiv:1206:0783] compares the low-temperature phase of the 3D Edwards-Anderson (EA) model to its mean-field counterpart, the Sherrington-Kirkpatrick (SK) model. The authors study the overlap distributions P_J(q) and conclude that the two models behave differently. Here we notice that a similar analysis using state-of-the-art, larger data sets for the EA model (generated with the Janus computer) leads to a very clear interpretation of the results of Yucesoy et al., showing that the EA model behaves as predicted by the replica symmetry breaking (RSB) theory.
We study the transition of short-range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the replicon, anomalous, and longitudinal modes. We discuss the symmetry of the theory in the limit of replica number $\stackrel{\ensuremath{\rightarrow}}{n}0,$ and consider the regular case where the longitudinal and anomalous masses remain degenerate. The spin-glass transitions in zero and nonzero fields are analyzed in a common framework. The mean-field treatment shows the usual results, that is a transition in zero field, where all the modes become critical, and a transition in nonzero field, at the de Almeida--Thouless (AT) line, with only the replicon mode critical. Renormalization group methods are used to study the critical behavior, to order $\ensuremath{\varepsilon}=6\ensuremath{-}d.$ In the general theory we find a stable fixed point associated with a spin-glass transition in a zero field. This fixed point becomes unstable in the presence of a small magnetic field, and we calculate crossover exponents, which we relate to zero-field critical exponents. In a finite magnetic field, we find no physical stable fixed point to describe the AT transition, in agreement with previous results of other authors.