2012/12/12 by Francesco Guerra, Guerra, Francesco
Economics, Econometrics and Finance · Materials Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Material Dynamics and Properties #Mathematical Physics (math-ph) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1212.2913
7 pages; in Field Theory and Collective Phenomena, S. De Lillo, P. Sodano, F.C. Khanna and G. Semenoff, eds., World Scientific, Singapore, 1995
arxiv created 2012/12/12 · openalex publication_date 2012/12/12 · arxiv updated 2012/12/13 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
In the Sherrington-Kirkpatrick mean field model for spin glasses, we show that the quenched average of the free energy can be expressed through a couple of functional order parameters, in a form very similar to the one found in the frame of the replica symmetry breaking method. The functional order parameters are implicitely given in terms of fluctuations of thermodynamic variables. Under the assumption that the two order parameters can be chosen to be the same, in the thermodynamic limit, it is shown that the Parisi free energy is a rigorous upper bound for the free energy of the model.