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Density and thermal corrections to the mass of the pions are studied in theframework of the SU(2) low energy effective chiral lagrangian, in terms of theisospin chemical potential $\mu_\tin{I}$. We concentrate the discussion in theregion where the isospin chemical potential (absolute value) becomes biggerthan the pion mass at zero temperature and density, i.e. in the phase where thecondensed $\pi^-$ phase appears (for negative chemical potential). We are ableto calculate the thermal and density evolution of masses in the limits where$|\mu_{I}|\gg m$ and where $|\mu_{I}| \gtrsim m$. We also identified the phasetransition curve.Comment: 12 pages, 13 figures. Published in Physical Review D7

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Thermal pion masses in the second phase:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mi>μ</mml:mi><mml:mi>I</mml:mi></mml:msub><mml:mo stretchy="false">|</mml:mo><mml:mo>&gt;</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mi>π</mml:mi></mml:msub></mml:math>

Thermal pion masses in the second phase:|μI|>mπ