Electronic Journal of Probability

No percolation in low temperature spin glass

Noam Berger and Ran J. Tessler

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 88, 19 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1508292259

Digital Object Identifier
doi:10.1214/17-EJP103

Mathematical Reviews number (MathSciNet)
MR3718716

Zentralblatt MATH identifier
1384.82005

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 82D40: Magnetic materials

Keywords
Edwards Anderson spin glass percolation

Rights
Creative Commons Attribution 4.0 International License.

Citation

Berger, Noam; Tessler, Ran J. No percolation in low temperature spin glass. Electron. J. Probab. 22 (2017), paper no. 88, 19 pp. doi:10.1214/17-EJP103. https://projecteuclid.org/euclid.ejp/1508292259


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