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.
The Mean Field Theory of Spin Glasses: The Heuristic Replica Approach and Recent Rigorous Results / Parisi, Giorgio. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 88:1-3(2009), pp. 255-269. [10.1007/s11005-009-0317-4]
The Mean Field Theory of Spin Glasses: The Heuristic Replica Approach and Recent Rigorous Results
PARISI, Giorgio
2009
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
