Critical behavior of the compactified lf4 theory

Abreu L.M., de Calan C., Santana A.E.

We investigate the critical behavior of the N-component Euclidean lf4 model, inthe large N limit, in three situations: confined between two parallel planes a distanceL apart from one another; confined to an infinitely long cylinder having asquare transversal section of area L2; and to a cubic box of volume L3. Taking themass term in the form m0 2 =asT−T0d, we retrieve Ginzburg-Landau models whichare supposed to describe samples of a material undergoing a phase transition,respectively, in the form of a film, a wire and of a grain, whose bulk transitiontemperature sT0d is known. We obtain equations for the critical temperature asfunctions of L and of T0, and determine the limiting sizes sustaining thetransition.