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In this work we consider the one-loop effective action of a self-interacting$\lambda\phi^{4}$ field propagating in a $D$ dimensional Euclidean spaceendowed with $d\leq D$ compact dimensions. The main purpose of this paper is tocompute the corrections to the mass of the field due to the presence of thecompactified dimensions. Although results for the one-loop correction to themass of a $\lambda\phi^{4}$ field are very well known for compactified toroidalspaces, where the field obeys periodic boundary conditions, similar results donot appear to be readily available for cases in which the scalar field issubject to Dirichlet and Neumann boundary conditions. We apply the results forthe one-loop mass correction to the study of the critical temperature inGinzburg-Landau models.

Some new results for the one-loop mass correction to the compactified $\lambda\phi^{4}$ theory