The chaotic phase at complex temperatures

Many systems have a phase in the complex temperature plane in which the partition function has a uniform density of zeros, and the thermodynamic free energy is non-analytical in temperature. The first example, which has been studied in depth analytically, is the Random Energy Model, but its interesting properties have been rather neglected. I will show how the physics of this phase is the relevant one to describe the " sign problem " of simulations, and also to understand the large fluctuations in the form factor of quantum systems that the Sachdev-Ye-Kitaev model.