A pedagagical introduction to the Lifshitz regime

TL;DR

This paper provides a pedagogical overview of phase diagrams in QCD, focusing on the Lifshitz point where disordered, ordered, and inhomogeneous phases meet, highlighting the importance of fluctuations beyond mean field theory.

Contribution

It introduces the concept of the Lifshitz point in QCD phase diagrams and discusses the significant impact of fluctuations, drawing analogies to inhomogeneous polymers.

Findings

Lifshitz points involve three phases: disordered, ordered, and inhomogeneous.

Fluctuations at the Lifshitz point significantly alter the phase diagram.

Analogies to polymer microemulsions provide insights into the Lifshitz regime.

Abstract

We give an elementary and pedagogical review of the phase diagrams which are possible in Quantum ChromoDynamics (QCD). Currently, the emphasis is upon the appearance of a critical endpoint, where disordered and ordered phases meet. In many models, though, a Lifshitz point also arises. At a Lifshitz point, three phases meet: disordered, ordered, and one where spatially inhomogeneous phases arise. At the level of mean field theory, the appearance of a Lifshitz point does not dramatically affect the phase diagram. We argue, however, that fluctuations about the Lifshitz point are very strong in the infrared, and significantly alter the phase diagram. We discuss at length the analogy to inhomogenous polymers, where the Lifshitz regime produces a bicontinuous microemulsion. We briefly mention the possible relevance to the phase diagram of QCD.