Fluctuations of the free energy of spherical Sherrington-Kirkpatrick model
Spherical Sherrington-Kirkpatrick (SSK) model is an example of disordered systems, called spin glasses. The free energy of 2-spin SSK, which is a random variable, is a finite temperature version of the largest eigenvalue of a random symmetric matrix. We show that the fluctuations of the free energy converge to the GOE Tracy-Widom distribution for the temperatures below a critical value. In the temperatures above the critical value, the limiting distribution is Gaussian. We also consider a SSK plus ferromagnetic Hamiltonian and discuss its relation with spiked random matrices. This is a joint work with Ji Oon Li.