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2019 Uniqueness and non-uniqueness for spin-glass ground states on trees
Johannes Bäumler
Electron. J. Probab. 24: 1-17 (2019). DOI: 10.1214/19-EJP323

Abstract

We consider a spin glass at temperature $T = 0$ where the underlying graph is a locally finite tree. We prove for a wide range of coupling distributions that uniqueness of ground states is equivalent to the maximal flow from any vertex to $\infty $ (where each edge $e$ has capacity $|J_{e}|$) being equal to zero which is equivalent to recurrence of the simple random walk on the tree.

Citation

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Johannes Bäumler. "Uniqueness and non-uniqueness for spin-glass ground states on trees." Electron. J. Probab. 24 1 - 17, 2019. https://doi.org/10.1214/19-EJP323

Information

Received: 9 November 2018; Accepted: 18 May 2019; Published: 2019
First available in Project Euclid: 16 July 2019

zbMATH: 07089015
MathSciNet: MR3991114
Digital Object Identifier: 10.1214/19-EJP323

Subjects:
Primary: 05C21, 05C81, 60K37, 82B44

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