What is the static Edwards-Anderson order parameter in the mean-field theory of spin glasses ?

Abstract

We present a replica derivation for the claim that the averaged square of the local spin expectation value in the long-range spin glass model is equal to the minimum, q(0) of Parisi's order parameters q(x). This corresponds to the dynamic interpretation of q(x) due to Sompolinsky. We show that q(0) obeys a power law q(0) ∼ b 2/3 for low external fields b and all temperatures 0 < T < Tc. Furthermore we calculate the low field magnetization for all temperatures. The calculations are based on an exact relation for the renormalized local susceptibility which replaces the Parisi-Toulouse hypothesis