Using the Matsubara formalism, we consider the massive (λϕ^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

more »

... an 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.