The Phase Diagram of the $N=2$ Kazakov-Migdal Model

TL;DR

This paper maps the phase diagram of the N=2 Kazakov-Migdal lattice model, revealing a line of first-order transitions ending at a critical point, and discusses implications for continuum limits and QCD relevance.

Contribution

It provides the first detailed phase diagram of the N=2 Kazakov-Migdal model, identifying the nature of phase transitions and the absence of a continuum limit except at the critical point.

Findings

Line of first-order phase transitions in (m_0, λ) plane

Critical point where the phase transition line ends

No continuum limit exists except at the critical end point

Abstract

We have determined the phase diagram of the simplest version of a lattice model introduced in the recent work of Kazakov and Migdal. If $m_0$ and $\lambda$ are the bare mass and self coupling of the scalar field in the model respectively, we find a line of first order phase transitions in the ($m_0, \lambda$) plane ending in a critical point where $\lambda$ is nonzero. Kazakov and Migdal speculate that their model of scalar field theory could induce QCD. Our work indicates that for $N=2$ there is no continuum limit for the Kazakov-Migdal model except at the critical end point. Whether or not a nontrivial continuum limit exists in the vicinity of the critical point requires careful study of the renormalization group properties of the model.