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The leading term for the average height of the barriers which could separatepure states in Ising spin glasses is calculated using instanton methods. It isfinite in dimensions $d < 6$. Replica symmetry breaking requires that thebarriers between pure states are infinite in the thermodynamic limit, as finitebarriers allow thermal mixing of pure states. As a consequence, a replicasymmetry broken phase cannot survive when $d < 6$. However, for $d > 6$ nosimilar instanton solution exists.

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