The Theory of Boundary Critical Phenomena

TL;DR

This paper introduces the theoretical framework of boundary critical phenomena, focusing on surface behaviors at bulk critical points across various systems, and discusses universality classes and boundary conditions using field theory.

Contribution

It provides a comprehensive theoretical overview of boundary critical phenomena, emphasizing the classification of surface universality classes and boundary conditions within the field-theoretical renormalization group approach.

Findings

Identification of key surface universality classes

Analysis of boundary conditions in field theories

Survey of short-distance singularities

Abstract

An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points of magnets, binary alloys, and fluids. Yet a multitude of related phenomena are mentioned. The most important distinct surface universality classes that may occur for a given universality class of bulk critical behavior are described, and the respective boundary conditions of the associated field theories are discussed. The short-distance singularities of the order-parameter profile in the diverse asymptotic regimes are surveyed.