Mathematics > Probability
[Submitted on 6 Dec 2018 (v1), last revised 16 Jul 2019 (this version, v2)]
Title:Uniqueness and Non-Uniqueness for Spin-Glass Ground States on Trees
View PDFAbstract: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.
Submission history
From: Johannes Bäumler [view email][v1] Thu, 6 Dec 2018 11:30:38 UTC (17 KB)
[v2] Tue, 16 Jul 2019 16:11:39 UTC (18 KB)
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