On the existence of a first order phase transition at small vacuum angle $\theta$ in the $CP^3$ model

TL;DR

This paper investigates the phase structure of the $CP^3$ model at small vacuum angles, demonstrating a first order phase transition and analyzing how the critical angle approaches zero in the infinite volume limit.

Contribution

It provides evidence for a first order phase transition at small $ heta$ in the $CP^3$ model and explores the behavior of the critical $ heta$ as the volume becomes infinite.

Findings

First order phase transition occurs at small $ heta$ in the $CP^3$ model.

Critical $ heta$ decreases towards zero as $eta$ increases.

Extrapolation to infinite volume shows the critical angle tends to zero.

Abstract

We examine the phase structure of the $CP^3$ model as a function of $\theta$ in the weak coupling regime. It is shown that the model has a first order phase transition at small $\theta$. We pay special attention to the extrapolation of the data to the infinite volume. It is found that the critical value of $\theta$ decreases towards zero as $\beta$ is taken to infinity.