Why replica symmetry breaking does not occur below six dimensions in Ising spin glasses

M. A. Moore

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arXiv · 1902.07099

Why replica symmetry breaking does not occur below six dimensions in Ising spin glasses

M. A. Moore

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Abstract

The leading term for the average height of the barriers which could separate pure states in Ising spin glasses is calculated using instanton methods. It is finite in dimensions $d < 6$. Replica symmetry breaking requires that the barriers between pure states are infinite in the thermodynamic limit, as finite barriers allow thermal mixing of pure states. As a consequence, a replica symmetry broken phase cannot survive when $d < 6$. However, for $d > 6$ no similar instanton solution exists.

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M. A. Moore. 2019-02-19. Why replica symmetry breaking does not occur below six dimensions in Ising spin glasses. https://arxiv.org/abs/1902.07099

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