  We consider an asymmetric 0-pi Josephson junction consisting of 0 and pi
regions of different lengths L_0 and L_pi. As predicted earlier this system can
be described by an effective sine-Gordon equation for the spatially averaged
phase psi so that the effective current-phase relation of this system includes
a \emph{negative} second harmonic ~sin(2 psi). If its amplitude is large
enough, the ground state of the junction is doubly degenerate psi=\pmvarphi,
where varphi depends on the amplitudes of the first and second harmonics. We
study the behavior of such a junction in an applied magnetic field H and
demonstrate that H induces an additional term ~H cos(psi) in the effective
current-phase relation. This results in a non-trivial ground state
\emph{tunable} by magnetic field. The dependence of the critical current on H
allows for revealing the ground state experimentally.
