Why replica symmetry breaking does not occur below six dimensions in Ising spin glasses
arXiv:1902.07099
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 . 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 . However, for no similar instanton solution exists.
arXiv comment5 pages, one figure. Further details added
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