Critical behaviour of the compactified $λφ^4$ theory

Details Critical behaviour of the compactified $λφ^4$ theory Critical behaviour of the compactified $λφ^4$ theory

2005-03-23

arxiv.org/abs/math-ph/0503057v1

J.Math.Phys. 46 (2005) 012304

Physics

Mathematical Physics

12 pages, no figures

Scientific paper

10.1063/1.1828589

We investigate the critical behaviour of the $N$-component Euclidean $\lambda \phi^4$ model at leading order in $\frac{1}{N}$-expansion. We consider it in three situations: confined between two parallel planes a distance $L$ apart from one another, confined to an infinitely long cylinder having a square cross-section of area $A$ and to a cubic box of volume $V$. Taking the mass term in the form $m_{0}^2=\alpha(T - T_{0})$, 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 ($T_{0}$) is known. We obtain equations for the critical temperature as functions of $L$ (film), $A$ (wire), $V$ (grain) and of $T_{0}$, and determine the limiting sizes sustaining the transition.

Affiliated with

Also associated with

No associations

Rating

Critical behaviour of the compactified $λφ^4$ theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Critical behaviour of the compactified $λφ^4$ theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Critical behaviour of the compactified $λφ^4$ theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-135198