Isospin Chemical potential and temperature effects in the Linear Sigma Model

In this letter we explore the temperature and isospin chemical potential ($\mu_I$) dependence of the vacuum structure and the meson masses in the linear sigma model, at the one loop level. The sigma meson mass grows steadily with temperature. This behavior does not agree with previous mean field calculations. For the pion our results show the same behavior as the mean field approach. The stability of the vacuum has a very soft dependence on $\mu_I$ since this is a second order effect in the tadpole diagrams.