Type: Article
Publication Date: 2014-02-06
Citations: 5
DOI: https://doi.org/10.1103/physrevd.89.036001
We present a derivation of an exact high temperature expansion for a one-loop thermodynamic potential $\mathrm{\ensuremath{\Omega}}(\stackrel{\texttildelow{}}{\ensuremath{\mu}})$ with complex chemical potential $\stackrel{\texttildelow{}}{\ensuremath{\mu}}$. The result is given in terms of a single sum, the coefficients of which are analytical functions of $\stackrel{\texttildelow{}}{\ensuremath{\mu}}$ consisting of polynomials and polygamma functions, decoupled from the physical expansion parameter $\ensuremath{\beta}m$. 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 $\stackrel{\texttildelow{}}{\ensuremath{\mu}}$ plane. Furthermore, our representation of $\mathrm{\ensuremath{\Omega}}(\stackrel{\texttildelow{}}{\ensuremath{\mu}})$ 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.