Continuous replica symmetry breaking in mean-field spin-glass models: Perturbation expansion without the replica trick

Abstract: The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. We introduce a perturbation expansion for a mean-field free-energy functional with a continuous order-parameter function. The expansion can be used to calculate all physical quantities in all mean-field spin-glass models and at all temperatures via standard methods of statistical mechanics, without the need to refer to the replica trick. The small expansion parameter is the difference between the continuous order-parameter function and the corresponding order parameter from the solution with one level of replica-symmetry breaking. In the talk I will introduce the approximation scheme used and present the results obtained for the first correction beyond the solution with one level of replica-symmetry breaking in the glassy phase of the Sherrington-Kirkpatrick model.

In collaboration with V. Janiš and A. Klíč. Published: Phys. Rev. B 87, 054201 (2013)