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

Abstract

Abstract We consider two-flavor chiral perturbation theory ( $$\chi $$ χ PT) at finite isospin chemical potential $$\mu _I$$ μ I and finite temperature T. We calculate the effective potential and the quark and pion condensates as functions of T and $$\mu _I$$ μ 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 $$\mu _I$$ μ I –T plane. Numerically, we find that the transition to the pion-condensed phase is second order in the region of validity of $$\chi $$ χ 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 $$\mu _I$$ μ I and find that $$\chi $$ χ PT seems to be converging very well.