Costanza Benassi

Thermodynamic Limit and Dispersive Regularisation in Matrix Models

Random matrix models provide a universal paradigm for the modelling of complex phenomena. We focus on the Hermitian Matrix Model and its phase diagram. We show this model supports the occurrence of a novel type of phase transition characterised by dispersive regularisation of the order parameter near the critical point. Using the identification of the partition function with a solution of the integrable system known as Volterra lattice, we argue that the singularity is resolved via the onset of a multidimensional dispersive shock of the order parameter in the space of coupling constants. This analysis explains the origin and mechanism leading to the emergence of chaotic behaviours observed in M^6 matrix models and extends its validity to even nonlinearity of arbitrary order. Based on a joint work with A. Moro (arXiv:1903.11473).