Field Theory, Critical Phenomena and Interfaces

TL;DR

This paper explores the deep connections between statistical mechanics and field theory, demonstrating their interplay through calculations and illustrating this with the critical behavior of a binary fluid system.

Contribution

It shows how concepts from field theory can be applied to analyze critical phenomena in statistical systems, specifically using binary fluid systems as an example.

Findings

Field theory effectively describes critical behavior in binary fluid systems.

Formal parallels between statistical mechanics and field theory are established.

Calculations demonstrate practical application of theoretical concepts.

Abstract

These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of actual calculations. To this purpose, the last section will demonstrate that a special statistical system, the binary fluid system, can be described by field theory in its critical behaviour.