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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(μ) with complex chemical potential μ. The result is given in terms of a single sum, the coefficients of which are analytical functions of μ 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 μ plane. Furthermore, our representation of Ω(μ) 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.

finite temperature field theory; thermodynamic potential; complex chemical potential

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