  Four-fermion interaction models are often used as simplified models of
interacting fermion fields with the chiral symmetry. The chiral symmetry is
dynamically broken for a larger four-fermion coupling. It is expected that the
broken symmetry is restored under extreme conditions. In this paper, the finite
size effect on the chiral symmetry breaking is investigated in the four-fermion
interaction model. We consider the model on a flat spacetime with a
compactified spatial coordinate, $\mathcal{M}^{D-1} \otimes S^1$ and obtain
explicit expressions of the effective potential for arbitrary spacetime
dimensions in the leading order of the $1/N$ expansion. Evaluating the
effective potential, we show the critical lines which divide the symmetric and
the broken phase and the sign-flip condition for the Casimir force.
