model [@gml] is thought to represent the long wavelength limit of QCD [@weinb; @gasl]. Much has been written about the model, both at zero temperature [@lee; @donob] and at finite temperature [@wil]. Despite this, the shape of the effective potential at both zero and finite temperature may have a nontrivial structure when the pion mass is nonzero, which feature seems to have escaped attention; at least it goes against the conventional considerations. In this section we explore the effective potential, and in the following sections we shall explore its phenomenological consequences.

The vacuum
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We use the sigma model in its linear representation. The Lagrangian is expressed in terms of a scalar field $\sigma$ and the pion field . $${\cal L} \,=\, \frac{1}{2}\left(\partial_{\mu}\sigma\right)^2
+ \frac{1}{2}\left(\partial_{\mu} \mbox{\boldmath $\pi$}\right)^2
-\frac{\lambda}{4} \left(\sigma^2 + \mbox{\boldmath $\pi$}^2 -
c^2/\lambda\right)^2 - V_{SB} \, .$$ The piece of the Lagrangian which explicitly breaks chiral symmetry is $V_{SB}$. In the absence of this term, the potential has the shape of the bottom of a wine bottle. Chiral symmetry is spontaneously broken in the vacuum, the pion is the massless Goldstone boson, and the $\sigma$ meson gets a mass on the order of 1-2 GeV. The axial vector current, 