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Exact high temperature expansion of the one-loop thermodynamic potential with complex chemical potential

We present a derivation of an exact high temperature expansion for a one-loop thermodynamic potential $Ω(\tildeμ)$ with complex chemical potential $\tildeμ$. The result is given in terms of a single sum the coefficients of which are analytical functions of $\tildeμ$ consisting of polynomials and polygamma functions, decoupled from the physical expansion parameter $βm$. The analytic structure of the coefficients permits us to explicitly calculate the thermodynamic potential for the imaginary chemical potential and analytically continue the domain to the complex $\tildeμ$ plane. Furthermore, our representation of $Ω(\tildeμ)$ is particularly well suited for the Landau--Ginzburg-type of phase transition analysis. This fact, along with the possibility of interpreting the imaginary chemical potential as an effective generalized-statistics phase, allows us to investigate the singular origin of the $m^3$ term appearing only in the bosonic thermodynamic potential.