No Percolation in low temperature spin glass

Noam Berger; Ran J. Tessler

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arXiv · 1610.02647

No Percolation in low temperature spin glass

Noam Berger·Ran J. Tessler

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Abstract

We consider the Edwards-Anderson Ising Spin Glass model for non negative temperatures T: We define the natural notion of Boltzmann- Gibbs measure for the Edwards-Anderson spin glass at a given temperature, and of unsatisfied edges. We prove that for low enough temperatures, in almost every spin configuration the graph formed by the unsatisfied edges is made of finite connected components. In other words, the unsatisfied edges do not percolate.

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Noam Berger, Ran J. Tessler. 2016-10-09. No Percolation in low temperature spin glass. https://arxiv.org/abs/1610.02647

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