Lattice QCD at finite isospin chemical potential and temperature

TL;DR

This paper investigates the phase transitions in lattice QCD at finite isospin chemical potential and temperature, identifying critical points and the nature of the transitions, including spontaneous pion condensation and its evaporation at high temperatures.

Contribution

It provides the first detailed lattice simulation analysis of QCD at finite isospin chemical potential, revealing the order of phase transitions and the behavior of the pion condensate.

Findings

Second order transition at critical isospin chemical potential with mean-field exponents

Pion condensate evaporates at a certain temperature for $> _c$

Transition order changes from second to first as chemical potential increases

Abstract

We simulate lattice QCD at a finite chemical potential $\mu_I$ for isospin ($I_3$) at zero and finite temperatures. At some $\mu_I=\mu_c$ QCD has a second order transition with mean-field critical exponents to a state where ($I_3$) is broken spontaneously by a charged pion condensate. Heating the system with $\mu_I > \mu_c$ we find there is some temperature at which this condensate evaporates. This transition appears to be second order and mean-field at lower $\mu_I$ values, and first order for $\mu_I$ sufficiently large. We are determining the dependence of the finite temperature crossover $T_c$ on $\mu_I$ for $\mu_I < \mu_c$. This is expected to be identical to $T_c$'s dependence on quark-number chemical potential $\mu_q$ for small $\mu_q$.