Distribution of frozen fields in the mean-field theory of spin glasses

Abstract

From a variational principle the authors derive a closed set of equations for the spin glass mean-field theory in terms of a local magnetisation on long timescales and a distribution of gradually frozen local fields. These equations are useful for deriving general relations and they find that the frozen field obeys a Langevin equation. Numerical solutions of the equations are obtained at T=0. The local field distribution shows a linear behaviour for small fields.