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

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.

5 pages, one figure. Further details added

References in corpus (3)

• Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions
• Free energy landscapes, dynamics and the edge of chaos in mean-field models of spin glasses
• Distribution of time scales in the Sherrington-Kirkpatrick model