Thermodynamic Limit and Dispersive Regularisation in Matrix Models

Costanza Benassi (Northumbria University)

Tuesday 10th March, 2020 16:00-17:00 Maths 311B


We show that Hermitian Matrix Models support the occurrence of a new 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 a reduction of the Toda hierarchy, known as Volterra system, we argue that the singularity is resolved via the onset of a multi-dimensional 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).

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