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

We consider two-flavor chiral perturbation theory (χPT) at finite isospin chemical potential μI and finite temperature T . We calculate the effective potential and the quark and pion condensates as functions of T and μI to nextto-leading order in the low-energy expansion in the presence of a pionic source. We map out the phase diagram in the μI –T plane. Numerically, we find that the transition to the pion-condensed phase is second order in the region of validity of χPT, 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 μI and find that χPT seems to be converging very well