Parisi formula for the ground state energy in the mixed \(p\)-spin model. (English) Zbl 1393.60116

The authors show that the thermodynamic limit of the ground state energy in the mixed \(p\)-spin model can be identified as a variational problem. This gives a natural generalization of the Parisi formula at zero temperature. As an open problem, they propose the question whether the methods of M. Talagrand [Ann. Math. (2) 163, No. 1, 221–263 (2006; Zbl 1137.82010)] and D. Panchenko [Ann. Probab. 42, No. 3, 946–958 (2014; Zbl 1292.82020)] can be applied to obtain their main result or not.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
60G15 Gaussian processes
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