The Sherrington-Kirkpatrick Model

By Dmitry Panchenko. 2013

494 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6adece29d0625c0710b0a60467acfdd76ab181d2

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In Condensed Matter Physics

In Statistical and Nonlinear Physics

Citations in the corpus

The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size (2019, methodology): “3 The Sherrington-Kirkpatrick (SK) model In this paper, we apply the QAOA to instances of the Sherrington-Kirkpatrick model, which is central to many important results in the theory of spin glass and disordered systems (see [7] for a review).”
Comparison and anti-concentration bounds for maxima of Gaussian random vectors (2013, unknown): “48 07 v3 [ m at h. PR ] 1 9 Fe b 20”
An Iterative Construction of Solutions of the TAP Equations for the Sherrington–Kirkpatrick Model (2012, methodology): “Panchenko, D.: The Sherrington–Kirkpatrick Model.”
Hypothesis Testing in High-Dimensional Regression Under the Gaussian Random Design Model: Asymptotic Theory (2013, unknown): “Attempts to make the replica method rigorous have been pursued over the last 30 years by some world-leading mathematicians [36, 37, 38, 39].”
Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors (2012, background): “ independent of j (i.e., εij =εi) and hence E[max1≤j≤p ε 4 ij]≤C1 in condition (E.4) reduces to E[ε4i]≤C1. Interestingly, these examples are also connected to spin glasses, see, for example, [41] and [33] (zij can be interpreted as generalized products of “spins” and εi as their random “interactions”
The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference (2018, background): “1 Introduction A very interesting development in probability theory in recent years has been the progress on a coherent mathematical theory [1, 2, 3, 4] of the predictions of the replica and cavity methods [5] in statistical physics of spin glasses.”
The Parisi formula for mixed $p$-spin models (2011, background): “n the model, but for simplicity of notation we will omit it. The proof we give here, obviously, assumes a certain level of expertise, but all the details starting from the foundations can be found in [16]. 2. Proof. Most of the ideas of the proof are well known and available in diﬀerent places in th”