Phases and triple (multiple) point: Critical phenomena around the AD singularity

Abstract

Continuing with our previous series of work, we present a case study of the critical phenomena around Argyres-Douglas singularity of $N=2$ susy made at $(A_1,A_{4k-1}),k=1,2$ realized by one-unitary matrix model. We determine the phase diagram, which is recast into LEEA of $N=2$, 4d gauge theory by the 0d-4d connection. There are three distinct phases, each corresponding to an eigenvalue distribution with 0, 1, and 2 gaps. These form an entire phase diagram with a triple point. Examining the behavior of the planar free energy, we show, among other things, that the transition line between 1- and 2-gap phases ending at the triple point is the $k=2$ multicritical one.