Condensates and pressure of two-flavor chiral perturbation theory at nonzero isospin and temperature

TL;DR

This paper uses two-flavor chiral perturbation theory to analyze the phase diagram, condensates, and pressure at finite isospin chemical potential and temperature, confirming second-order transitions and good convergence of the expansion.

Contribution

It provides a detailed next-to-leading order analysis of the phase diagram and thermodynamic properties of two-flavor $ ext{chiPT}$ at nonzero isospin and temperature, including pressure calculations.

Findings

Transition to pion-condensed phase is second order.

$ ext{chiPT}$ shows good convergence at two-loop order.

Phase diagram mapped out in the $\mu_I$--$T$ plane.

Abstract

We consider two-flavor chiral perturbation theory ($\chi$PT) at finite isospin chemical potential $\mu_I$ and finite temperature $T$. We calculate the effective potential and the quark and pion condensates as functions of $T$ and $\mu_I$ to next-to-leading order in the low-energy expansion in the presence of a pionic source. We map out the phase diagram in the $\mu_I$--$T$ plane. Numerically, we find that the transition to the pion-condensed phase is second order in the region of validity of $\chi$PT, which is in agreement with model calculations and lattice simulations. Finally, we calculate the pressure to two-loop order in the symmetric phase for nonzero $\mu_I$ and find that $\chi$PT seems to be converging very well.