Phase structure of the $O(2)$ ghost model with higher-order gradient term

Understand

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.