Approximate Ultrametricity for Random Measures and Applications to Spin Glasses

DOI10.1002/cpa.21685zbMath1361.60035arXiv1412.7076OpenAlexW3101100134MaRDI QIDQ2976156

Aukosh Jagannath

Publication date: 13 April 2017

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.7076

zbMATH Keywords

spin glassesconvergence in lawrandom measuresapproximate ultrametricityRuelle probability cascade

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Random measures (60G57)

Related Items (18)

Poisson-Dirichlet statistics for the extremes of a randomized Riemann zeta function ⋮ On the TAP free energy in the mixed \(p\)-spin models ⋮ The algorithmic hardness threshold for continuous random energy models ⋮ The geometry of the Gibbs measure of pure spherical spin glasses ⋮ Generalized TAP Free Energy ⋮ The TAP free energy for high-dimensional linear regression ⋮ Ultrametricity in spin glasses ⋮ Features of a spin glass in the random field Ising model ⋮ Shattering versus metastability in spin glasses ⋮ Optimizing mean field spin glasses with external field ⋮ On the TAP equations via the cavity approach in the generic mixed \(p\)-spin models ⋮ Localization in Gaussian disordered systems at low temperature ⋮ Average Gromov hyperbolicity and the Parisi ansatz ⋮ Approximate ground states of hypercube spin glasses are near corners ⋮ Geometry of the Gibbs measure for the discrete 2D Gaussian free field with scale-dependent variance ⋮ The overlap gap property in principal submatrix recovery ⋮ Thouless-Anderson-Palmer equations for generic \(p\)-spin glasses ⋮ Ultrametric fitting by gradient descent ^*

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