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

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.