  We consider the vacuum structure of two-dimensional $\phi^4$ theory on
$S^{1}/Z_{2}$ both in the bosonic and the supersymmetric cases. When the size
of the orbifold is varied, a phase transition occurs at $L_{c}=2\pi/m$, where
$m$ is the mass of $\phi$. For $L<L_{c}$, there is a unique vacuum, while for
$L>L_{c}$, there are two degenerate vacua. We also obtain the 1-loop quantum
corrections around these vacuum solutions, exactly in the case of $L<L_{c}$ and
perturbatively for $L$ greater than but close to $L_{c}$. Including the
fermions we find that the "chiral" zero modes around the fixed points are
different for $L<L_{c}$ and $L>L_{c}$. As for the quantum corrections, the
fermionic contributions cancel the singular part of the bosonic contributions
at L=0. Then the total quantum correction has a minimum at the critical length
$L_{c}$.
