Finite-temperature phase transitions of third and higher order in gauge theories at large $N$

Understand

We study phase transitions in $SU(\infty)$ gauge theories at nonzero temperature using matrix models.

• Our basic assumption is that the effective potential is dominated by double trace terms for the Polyakov loops.
• As a function of the various parameters, related to terms linear, quadratic, and quartic in the Polyakov loop, the phase diagram exhibits a universal structure.
• In a large region of this parameter space, there is a continuous phase transition whose order is larger than second.