Local field distributions in spin glasses

We revisit the concept of marginal stability in glasses, and determine its range of applicability in the context of avalanche-type response to slow external driving. We argue that there is an intimate connection between a pseudo-gap in the distribution of local fields and crackling in systems with long-range interactions. We show how the principle of marginal stability offers a unifying perspective on the phenomenology of systems as diverse as spin and electron glasses, hard spheres, pinned elastic interfaces and the plasticity of soft amorphous solids.

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“…of the pseudo-gap, implying that the constraint is just marginally satisfied with θ = 1 [39,43]. In Sec.…”

Section: Spin Glassesmentioning

confidence: 86%

Marginal Stability in Structural, Spin, and Electron Glasses

Müller

Wyart

2015

Annu. Rev. Condens. Matter Phys.

180

264

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“…Thus, extending RSB to glassy systems on sparse networks, i.e., random graphs [17] of finite average or fixed degree ("Bethe lattices", BL), constituted another major breakthrough [18]. More recently, the one-dimensional long-range model [19] has gained popularity in numerical studies [20][21][22][23] for the ability to interpolate between SK and the EA (but on a 1d -ring geometry) based on the range of interactions. That model has effective upper and lower dimensions, but all results obtained are numerical.…”

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confidence: 99%

Ground State Properties of the Diluted Sherrington-Kirkpatrick Spin Glass

Boettcher

2020

Phys. Rev. Lett.

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We present a numerical study of ground states of the dilute versions of the Sherrington-Kirkpatrick (SK) mean-field spin glass. In contrast to so-called "sparse" mean-field spin glasses that have been studied widely on random networks of finite (average or regular) degree, the networks studied here are randomly bond-diluted to an overall density p, such that the average degree diverges as ∼ pN with the system size N . Ground-state energies are obtained with high accuracy for random instances for given p over a wide range of densities p. Since this is a NP-hard combinatorial problem, we employ the Extremal Optimization heuristic to that end. We find that the exponent describing the finite-size corrections, ω, varies continuously with p, a somewhat surprising result, as one would not expect that gradual bond-dilution would change the universality class of a statistical model. For p → 1, the familiar result of ω(p = 1) ≈ 2 3 for SK is obtained. In the limit of small p, ω(p) appears to diverge hyperbolically. arXiv:1912.04974v1 [cond-mat.dis-nn]

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“…There is also a factor 2 that arises from the fact that the rigidity is calculated as an energy difference. The distribution of local fields at T = 0 has been calculated for the EAG in 2D and 3D, and the curves are very similar to the distribution of local rigidities [36]. The rigidity distribution P L (r) [ Fig.…”

Section: A Rigidity Distributionmentioning

confidence: 85%

Backbone structure of the Edwards-Anderson spin-glass model

Romá

Risau-Gusmán

2013

Phys. Rev. E

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We study the ground-state spatial heterogeneities of the Edwards-Anderson spin-glass model with both bimodal and Gaussian bond distributions. We characterize these heterogeneities by using a general definition of bond rigidity, which allows us to classify the bonds of the system into two sets, the backbone and its complement, with very different properties. This generalizes to continuous distributions of bonds the well-known definition of a backbone for discrete bond distributions. By extensive numerical simulations we find that the topological structure of the backbone for a given lattice dimensionality is very similar for both discrete and continuous bond distributions. We then analyze how these heterogeneities influence the equilibrium properties at finite temperature and we discuss the possibility that a suitable backbone picture can be relevant to describe spin-glass phenomena.

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Local field distributions in spin glasses

Cited by 24 publications

References 41 publications

Marginal Stability in Structural, Spin, and Electron Glasses

Marginal Stability in Structural, Spin, and Electron Glasses

Ground State Properties of the Diluted Sherrington-Kirkpatrick Spin Glass

Backbone structure of the Edwards-Anderson spin-glass model

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