Critical behavior of the compactified lf4 theory

Abstract

We investigate the critical behavior of the N-component Euclidean lf4 model, in the large N limit, in three situations: confined between two parallel planes a distance L apart from one another; confined to an infinitely long cylinder having a square transversal section of area L2; and to a cubic box of volume L3. Taking the mass term in the form m0 2 =asT−T0d, we retrieve Ginzburg–Landau models which are 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 transition temperature sT0d is known. We obtain equations for the critical temperature as functions of L and of T0, and determine the limiting sizes sustaining the transition. © 2005 American Institute of Physics.