In this paper we consider the CPN−1 model confined to an interval of finite size at finite temperature and chemical potential. We compute, in the large-N approximation, the one-loop effective action of the order parameter associated with the effective mass of the quantum fluctuations. To discuss some generic features of the ground state of the model, we work out a mixed-gradient expansion and obtain an expression for the thermodynamic potential density as a functional of the order parameter, generalizing previous calculations to arbitrarily large order and to the case of small finite density. The technique used here relies on analytic regularization and provides an efficient scheme to extract the coefficients of the expansion. These coefficients are then used to deduce some generic properties of the ground state as a function of external conditions. For vanishing chemical potential and intervals of any size, we show that inhomogeneous phases are not energetically favored, but we find evidence that they may become energetically favored for large enough values of the chemical potential. We also show that there can be no transition to a massless phase for any value of the external conditions and clarify a seemingly important point regarding the regularization of the effective action connected to the appearance of logarithmic divergences and to the Mermin-Wagner-Hoenberg-Coleman theorem.
|Publication status||Published - 2019 Dec 27|
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