Abstract: Spin glasses are disordered magnetic systems that have played an important role in probability theory, statistical mechanics, and mathematical physics for several decades. While the classical Sherrington–Kirkpatrick (SK) model is by now fairly well understood, much less is known about its quantum counterpart, where random disorder competes with quantum fluctuations. In this talk, I will give an introduction to quantum mean-field spin glasses, focusing in particular on the SK model in a transverse magnetic field. 

I will explain how probabilistic representations allow one to reformulate these quantum systems in terms of classical, continuous vector spin glasses. This then enables a Parisi variational formulation of their free energy. I will then survey several recent mathematical results concerning the phase diagram of the Quantum SK: in contrast to its classical counterpart, it exhibits a phase transition at zero temperature. 

The talk is based on several works with Chokri Manai (NYU).