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

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.

Comments: 11 pages and 6 figures, LaTeX; typos corrected, references added