Correlations among discontinuities in QCD phase diagram

TL;DR

This paper explores how discontinuities in one order parameter in the QCD phase diagram imply similar discontinuities in others, analyzing conditions for coexistence and providing model-based examples.

Contribution

It clarifies the conditions under which discontinuities of different orders coexist in QCD phase transitions and demonstrates this with the PNJL model.

Findings

Discontinuities in one order parameter induce similar discontinuities in others.

Coexistence of different order discontinuities occurs when certain conditions are met.

Examples of same-order discontinuity coexistence are shown in both imaginary and real chemical potential regions.

Abstract

We show, in general, that when a discontinuity of either zeroth-order or first-order takes place in an order parameter such as the chiral condensate, discontinuities of the same order emerge in other order parameters such as the Polyakov loop. A condition for the coexistence theorem to be valid is clarified. Consequently, only when the condition breaks down, zeroth-order and first-order discontinuities can coexist on a phase boundary. We show with the Polyakov-loop extended Nambu--Jona-Lasinio model that such a type of coexistence is realized in the imaginary chemical potential region of the QCD phase diagram. We also present examples of coexistence of the same-order discontinuities in the real chemical potential region.