The mean field theory of spin glasses: the heuristic replica approach and recent rigorous results

Details The mean field theory of spin glasses: the heuristic replica approach and recent rigorous results The mean field theory of spin glasses: the heuristic replica approach and recent rigorous results

2009-12-06

arxiv.org/abs/0912.1127v1

Letters in Mathematical Physics 91, 255 (2009)

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 1 figure; lecture at the Flato Colloquia Day, Thursday 27 November, 2008

Scientific paper

10.1007/s11005-009-0317-4

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.

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