Multicritical Behavior of $c=1$ Matrix Model

TL;DR

This paper investigates the multicritical behavior of the $c=1$ matrix model, extending previous work to include higher genus contributions and nonperturbative completions, revealing a surprising scaling behavior.

Contribution

It provides a nonperturbative completion for odd multicritical points using WKB wave functions, extending the understanding of $c=1$ matrix models.

Findings

Higher genus contributions determined for odd multicriticality

Nonperturbative completion derived from WKB wave functions

Identical expressions for scaled chemical potential as at lowest critical point

Abstract

We discuss multicritical behavior of $c=1$ matrix model, extending the recent work of ref. \cite{CIO} on a nonperturbative completion of the density of states function. For the odd orders of multicriticality, we are able to determine the higher genus contributions and a nonperturbative completion from the WKB wave function of the multicritical periodic potential. The expression for the contributions as a function of the scaled chemical potential is found to be the same as the one at the lowest critical point. We point out a strange scaling behavior.