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Random matrices and complexity of spin glasses. (English) Zbl 1269.82066
A question of interest in the theory of spin glasses is the following. How many critical values does a typical random Morse function have on a high-dimensional manifold?
The authors propose some answers, and to this end derive an asymptotic evaluation of the complexity of spherical \(p\)-spin glass models by using symmetric random matrices with independent Gaussian.

MSC:
82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)
15B52 Random matrices (algebraic aspects)
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