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

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

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