Integrable Systems and Random Matrix Theory Seminar

We consider a spherical spin system with pure 2-spin spherical Sherrington-Kirkpatrick (SSK) Hamiltonian with ferromagnetic Curie-Weiss interaction. This model shows a two-dimensional phase transition with respect to the temperature and the coupling strength. Using the results of random matrix theory and steepest descent method, we investigate the fluctuation of free energy when the temperature is scaled with the system size and approaches the critical line between paramagnetic and ferromagnetic regimes. In the talk, I will first briefly present the history and known results of spin-glass. Then the phase diagram of the SSK model with ferromagnetic interaction will be discussed. If time permits, we will discuss invoked questions such as the independence of fluctuations of linear statistics and leading eigenvalues of rank 1 spiked random matrices. Speaker(s): Hao Wu (University of Michigan)