Weighted averages and order parameters for the infinite range Ising spin glass

Abstract

The Sherrington-Kirkpatrick spin glass model (1975) is studied by replicas and by analysing the mean field equations of Thouless, Anderson and Palmer (TAP) (1977). The authors show that the standard order parameter defined by statistical mechanics is given by the average of all off-diagonal components of the matrix q_{alpha beta} . There is consequently no violation of the fluctuation dissipation theorem. They describe how to weight the different solutions of the TAP equations and argue that there is no entropy from solution degeneracy. This assumption is shown to be internally consistent. The square of a spin expectation value for a solution, averaged over solutions, is shown to be q(1) if they make the Parisi-Sompolinsky ansatz for q_{alpha beta} .