Phase structure of 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 model with higher-order derivatives, revealing phase transitions and comparing with standard models using renormalization group analysis.

Contribution

It introduces the analysis of a ghost scalar field model with higher-order derivatives and identifies its phase structure and transition characteristics.

Findings

Identified symmetric and ghost condensate phases.

Finiteness of correlation length suggests first-order phase transition.

Compared phase behavior with ordinary $O(2)$ scalar field model.

Abstract

The phase structure and the infrared behaviour of the Euclidean 3-dimensional $O(2)$ symmetric ghost scalar field model with higher-order derivative term has been investigated in Wegner and Houghton's renormalization group framework. The symmetric phase in which no ghost condensation occurs and the phase with restored symmetry but with a transient presence of a ghost condensate have been identified. Finiteness of the correlation length at the phase boundary hints to a phase transition of first order. The results are compared with those for the ordinary $O(2)$ symmetric scalar field model.