A New Perturbation Theory of Finite-Size Effects Near Critical Point

TL;DR

This paper introduces a simplified perturbation theory for analyzing finite-size effects near critical points in the $^4$ model, applicable above and below the critical temperature, avoiding renormalization.

Contribution

The paper presents a novel perturbation approach based on generating functionals that simplifies calculations and eliminates the need for renormalization near critical points.

Findings

Simplifies finite-size effect calculations near critical points.

Applicable for temperatures both above and below the critical point.

Avoids renormalization in computing physical quantities.

Abstract

A new perturbation theory is proposed for studying finite-size effects near critical point of the $\phi^4$ model with a one-component order parameter. The new approach is based on the techniques of generating functional and functional derivative with respect to external source field and can be used for temperatures both above and below the critical point of the bulk system. It is shown that this approach is much simpler comparing with available perturbation theories. Particularly, this new method avoids renormalization in calculating many physical quantities such as correlation functions etc..