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The Mean Field Theory of Spin Glasses: The Heuristic Replica Approach and Recent Rigorous Results

  • Giorgio Parisi
Article

Abstract

The mathematically correct computation of the spin glasses free energy in the infinite range limit crowns 25 years of mathematic efforts in solving this model. The exact solution of the model was found many years ago by using a heuristic approach; the results coming from the heuristic approach were crucial in deriving the mathematical results. The mathematical tools used in the rigorous approach are quite different from those of the heuristic approach. In this note we will review the heuristic approach to spin glasses in the light of the rigorous results; we will also discuss some conjectures that may be useful to derive the solution of the model in an alternative way.

Mathematics Subject Classification (2000)

11E95 46N30 60F10 82B44 

Keywords

p-adic theory applications in probability theory and statistics large deviations disordered systems (random Ising models, random Schrödinger operators, etc.) 

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Copyright information

© Springer 2009

Authors and Affiliations

  1. 1.Dipartimento di Fisica, Sezione INFN, SMC of INFM-CNRUniversità di Roma “La Sapienza”RomeItaly

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