Boundary dependence of the coupling constant and the mass in the vector N-component (λvarphi4)D theory

Abstract

Using the Matsubara formalism, we consider the massive (λvarphi4)D vector N-component model in the large-N limit, the system being confined between two infinite parallel planes. We investigate the behaviour 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 formulae for the L-dependent renormalized coupling constant and mass are obtained in D = 3 and their behaviours as functions of L are displayed. We are also able to obtain, 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 an implicit formula for the critical L is given.