Open Access
2017 No percolation in low temperature spin glass
Noam Berger, Ran J. Tessler
Electron. J. Probab. 22: 1-19 (2017). DOI: 10.1214/17-EJP103


We consider the Edwards-Anderson Ising Spin Glass model for temperatures $T\geq 0.$ We define notions of Boltzmann-Gibbs measure for the Edwards-Anderson spin glass at a given temperature, and of unsatisfied (frustrated) edges, and recall the notion of ground states. We prove that for low positive temperatures, in almost every spin configuration the graph formed by the unsatisfied edges is made of finite connected components. Similarly, for zero temperature, we show that in almost every ground state the graph of unsatisfied edges is a forest all of whose components are finite. In other words, for low enough temperatures the unsatisfied edges do not percolate.


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Noam Berger. Ran J. Tessler. "No percolation in low temperature spin glass." Electron. J. Probab. 22 1 - 19, 2017.


Received: 8 June 2017; Accepted: 4 September 2017; Published: 2017
First available in Project Euclid: 18 October 2017

zbMATH: 1384.82005
MathSciNet: MR3718716
Digital Object Identifier: 10.1214/17-EJP103

Primary: 60K35 , 82B20 , 82D40

Keywords: Edwards Anderson , percolation , Spin glass

Vol.22 • 2017
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