Regensburg 2013 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 25: Critical Phenomena and Phase Transitions

DY 25.7: Vortrag

Donnerstag, 14. März 2013, 11:15–11:30, H46

Continuous replica-symmetry breaking in mean-field spin-glass models: Perturbation expansion without the replica trick — Vaclav Janis, •Anna Kauch, and Antonin Klic — Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 18221 Praha, Czech Republic

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. The averaged physical quantities are to be represented via the replica trick and the limit to zero number of replicas is to be performed for each of them. To avoid this we introduce a perturbation expansion for a mean-field free-energy functional with a continuous order-parameter function without the need to refer to the replica trick. The expansion can be used to calculate all physical quantities in all mean-field spin-glass models and at all temperatures, including zero temperature. The small expansion parameter is a difference between the continuous order-parameter function and the corresponding order parameter from the solution with one level of replica-symmetry breaking. The first correction beyond the approximation with one level of replica-symmetry breaking is explicitly evaluated in the glassy phase of the Sherrington-Kirkpatrick model.