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We consider the $\frac{\lambda}{4!}(\phi^{4}_{1}+\phi^{4}_{2})$ model on ad-dimensional Euclidean space, where all but one of the coordinates areunbounded. Translation invariance along the bounded coordinate, z, which liesin the interval [0,L], is broken because of the boundary conditions (BC's)chosen for the hyperplanes z=0 and z=L. Two different possibilities for theseBC's boundary conditions are considered: DD and NN, where D denotes Dirichletand N Newmann, respectively. The renormalization procedure up to one-loop orderis applied, obtaining two main results. The first is the fact that therenormalization program requires the introduction of counterterms which aresurface interactions. The second one is that the tadpole graphs for DD and NNhave the same z dependent part in modulus but with opposite signs. Weinvestigate the relevance of this fact to the elimination of surfacedivergences.Comment: 33 pages, 2 eps figure

Finite size effects in the anisotropic (λ/4!)(φ14+φ24)d model