In search of diabolical critical points

TL;DR

This paper explores higher-codimension topological defects in phase diagrams, introducing diabolical critical points (DCPs) as a new class of stable, non-trivial winding phenomena in classical and quantum systems.

Contribution

It defines diabolical critical points (DCPs), analyzes their stability conditions, and provides examples in (1+1)-dimensional quantum systems, extending the concept of phase transition defects.

Findings

DCPs exist in classical statistical systems.

Stable DCPs can occur in (1+1)-D quantum systems.

Conditions for the stability of DCPs are proposed.

Abstract

A phase transition is an example of a ``topological defect'' in the space of parameters of a quantum or classical many-body systems. In this paper, we consider phase diagram topological defects of higher codimension. These have the property that equilibrium states undergo some kind of non-trivial winding as one moves around the defect. We show that such topological defects exist even in classical statistical mechanical systems, and describe their general structure in this context. We then introduce the term ``diabolical critical point'' (DCP), which is a higher-codimension analog of a continuous phase transition, with the proximate phases of matter replaced by the non-trivial winding of the proximate equilibrium states. We propose conditions under which a system can have a stable DCP. We also discuss some examples of stable DCPs in (1+1)-dimensional quantum systems.