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

The phase structure and the infrared behaviour of the Euclidean 3-dimensional $O(2)$ symmetric ghost scalar field $\varphi$ 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.