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2020 Free energy of multiple systems of spherical spin glasses with constrained overlaps
Justin Ko
Electron. J. Probab. 25: 1-34 (2020). DOI: 10.1214/20-EJP431

Abstract

The free energy for multiple systems of spherical spin glasses with constrained overlaps was first studied in [10]. In [24] the authors proved an upper bound of the constrained free energy using Guerra’s interpolation. In this paper, we prove this upper bound is sharp. Our approach combines the ideas of the Aizenman–Sims–Starr scheme in [4] and the synchronization mechanism used in the vector spin models in [22] and [23]. We derive a vector version of the Aizenman–Sims–Starr scheme for spherical spin glass and use the synchronization property of arrays obeying the overlap-matrix form of the Ghirlanda–Guerra identities to prove the matching lower bound.

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Justin Ko. "Free energy of multiple systems of spherical spin glasses with constrained overlaps." Electron. J. Probab. 25 1 - 34, 2020. https://doi.org/10.1214/20-EJP431

Information

Received: 2 May 2019; Accepted: 8 February 2020; Published: 2020
First available in Project Euclid: 21 February 2020

zbMATH: 1437.60075
MathSciNet: MR4073689
Digital Object Identifier: 10.1214/20-EJP431

Subjects:
Primary: 60F10, 60G15, 60K35, 82B44

JOURNAL ARTICLE
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