Thermodynamic Limit and Dispersive Regularisation in Matrix Models
Abstract
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 by 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.
Cite
@article{arxiv.1903.11473,
title = {Thermodynamic Limit and Dispersive Regularisation in Matrix Models},
author = {Costanza Benassi and Antonio Moro},
journal= {arXiv preprint arXiv:1903.11473},
year = {2020}
}
Comments
8 pages, 7 figures. Sections have been reorganised and expanded. Order of figures and captions have been modified. Accepted for publication in Physical Review E