  It is known that the symmetric (massless) state of the Nambu--Jona-Lasinio
model in 2+1 dimensions in a magnetic field B is not the ground state of the
system at zero temperature due to the presence of a negative, linear in
&|\sigma+i\pi|$, term in the effective potential for the composite fields
$\sigma\sim\bar{\psi}\psi$ and $\pi\sim\bar{\psi}i\gamma^5\psi$, while the
quadratic term is always positive (a tachyon is absent). We find that finite
temperature is a necessary ingredient for the tachyonic instability of the
symmetric state to occur. Utilizing the Schwinger--Keldysh real-time formalism
we calculate the dispersion relations for the fluctuation modes of the
composite fields $\sigma$ and $\pi$. We demonstrate the presence of the
tachyonic instability of the symmetric state for coupling constant that exceeds
a certain critical value which vanishes as temperature tends to zero in
accordance with the phenomenon of magnetic catalysis.
