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arXiv · 1812.02469

Uniqueness and Non-Uniqueness for Spin-Glass Ground States on Trees

Johannes Bäumler
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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.

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BibTeXRIS

Johannes Bäumler. 2018-12-06. Uniqueness and Non-Uniqueness for Spin-Glass Ground States on Trees. https://doi.org/10.1214/19-ejp323

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