Equation of state and coarse grained free energy for matrix models

TL;DR

This paper studies phase transitions in 3D scalar matrix models, especially complex 2x2 matrices, deriving the universal equation of state for weak first order transitions and analyzing coarse grained free energy to assess bubble nucleation validity.

Contribution

It provides the first computation of the universal equation of state for weak first order phase transitions in matrix models and examines coarse graining effects on bubble nucleation.

Findings

Universal equation of state for weak first order transitions derived

Coarse grained free energy dependence analyzed

Quantitative criterion for bubble nucleation validity established

Abstract

We investigate phase transitions in three dimensional scalar matrix models, with special emphasis on complex $2 \times 2$ matrices. The universal equation of state for weak first order phase transitions is computed. We also study the coarse grained free energy. Its dependence on the coarse graining scale gives a quantitative criterion for the validity of the standard treatment of bubble nucleation.