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Setting Limits on Supersymmetry Using Simplified Models
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Thermodynamic limit and dispersive regularization in matrix models.

Costanza Benassi1, Antonio Moro1

  • 1Department of Mathematics, Physics and Electrical Engineering, Northumbria University Newcastle, Newcastle upon Tyne NE1 8ST, United Kingdom.

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Summary
This summary is machine-generated.

Hermitian matrix models exhibit a phase transition with dispersive regularization. This resolves singularities via dispersive shocks, explaining chaotic behavior in M^6 matrix models and other nonlinear systems.

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Area of Science:

  • * Theoretical Physics
  • * Mathematical Physics

Background:

  • * Hermitian matrix models are crucial in quantum field theory and statistical mechanics.
  • * Understanding phase transitions and emergent phenomena like chaos is a key challenge.

Purpose of the Study:

  • * To investigate the nature of phase transitions in Hermitian matrix models.
  • * To explain the mechanism behind chaotic behavior in these models.

Main Methods:

  • * Analysis of the partition function using the Volterra system, a reduction of the Toda hierarchy.
  • * Characterization of the order parameter's behavior near the critical point.

Main Results:

  • * Discovery of a phase transition characterized by dispersive regularization of the order parameter.
  • * Identification of a multidimensional dispersive shock resolving the singularity in coupling constant space.
  • * Explanation of the origin of chaotic behaviors in M^6 matrix models.

Conclusions:

  • * The study provides a unified mechanism for chaotic behavior in matrix models.
  • * The findings extend to systems with arbitrary order nonlinearity.
  • * Dispersive regularization and shocks are key to understanding these complex phenomena.