Existence of Full Replica Symmetry Breaking for the Sherrington-Kirkpatrick Model at Low Temperature

Abstract

We prove the existence of full replica symmetry breaking (FRSB) for the Sherrington-Kirkpatrick (SK) model at low temperature. More specifically, we prove that slightly beyond the critical temperature, the Parisi measure for the SK model is supported on an interval starting at the origin and only has one jump discontinuity at the right endpoint.