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We calculate the light quark condensate, the strange quark condensate, thepion condensate, and the axial condensate in three-flavor chiral perturbationtheory ($\chi$PT) in the presence of an isospin chemical potential atnext-to-leading order at zero temperature. It is shown that the three-flavor$\chi$PT effective potential and condensates can be mapped onto two-flavor$\chi$PT ones by integrating out mesons with strange quark content (kaons andeta), with renormalized couplings. We compare the results for the light quarkand pion condensates at finite pseudoscalar source with ($2+1$)-flavor latticeQCD, and we also compare the axial condensate at zero pseudoscalar and axialsources with lattice QCD data. We find that the light quark, pion, and axialcondensates are in very good agreement with lattice data. There is an overallimprovement by including NLO effects.

Quark, pion and axial condensates in three-flavor finite isospin chiral perturbation theory