Triple point in the $O(2)$ ghost model with higher-order gradient term

TL;DR

This paper investigates the phase structure of a 3D $O(2)$ ghost scalar field with higher-order derivatives, revealing a triple point and different phase transitions using a renormalization group approach.

Contribution

It introduces the effect of higher-derivative couplings in the $O(2)$ ghost model, identifying a triple point and characterizing phase transitions within an RG framework.

Findings

Higher-derivative coupling induces three distinct phases.

A triple point in the phase diagram is identified.

Different types of phase transitions are characterized.

Abstract

The phase structure and the infrared behaviour of the Euclidean 3-dimensional $O(2)$ symmetric ghost scalar field $\phi$ has been investigated in Wegner and Houghton's renormalization group framework, including higher-derivatives in the kinetic term. It is pointed out that higher-derivative coupling provides three phases and leads to a triple point in that RG scheme. The types of the phase transitions have also been identified.