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.

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

References in corpus (4)

• Melting Crystal, Quantum Torus and Toda Hierarchy
• On Hamiltonian perturbations of hyperbolic systems of conservation laws
• Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure
• On quantum and relativistic mechanical analogues in mean field spin models

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