  Using the Matsubara formalism, we consider the massive $(\lambda
\phi^{4})_{D}$ vector $N$-component model in the large $N$ limit, the system
being confined between two infinite paralell planes. We investigate the
behavior of the coupling constant as a function of the separation $L$ between
the planes. For the Wick-ordered model in $D = 3$ we are able to give an exact
formula to the $L$-dependence of the coupling constant. For the
non-Wick-ordered model we indicate how expressions for the coupling constant
and the mass can be obtained for arbitrary dimension $D$ in the small-$L$
regime. Closed exact formulas for the $L$-dependent renormalized coupling
constant and mass are obtained in $D = 3$ and their behaviors as functions of
$L$ are displayed. We are also able to obtainn in generic dimension $D$, an
equation for the critical value of $L$ corresponding to a second order phase
transition in terms of the Riemann $zeta$-function. In $D = 3$ a
renormalization is done and an explicit formula for the critical $L$ is given.
