  Thermodynamic properties of systems with repulsive interactions, are
considered in the grand canonical ensemble. The analytic structure of the
excluded-volume model in the complex plane of the system chemical potential
(fugacity) is elaborated, based on the fact that the pressure function can be
given in terms of the Lambert W-function. Even though the excluded volume model
has no phase transitions at real values of the chemical potential, it does
exhibit a branch cut singularity in the complex plane, thus limiting the
convergence range of the Taylor expansion in the chemical potential. Close
similarities to analytic properties of the other models with repulsive
interactions, such as a cluster expansion model, the mean-field model, and the
ideal Fermi gas model, are pointed out. As an example, repulsive baryonic
interactions in a hadron gas, with a focus on the fugacity/virial and Taylor
expansion methods used in lattice QCD, are presented. The asymptotic behavior
of the Fourier expansion coefficients in these various models suggests that the
singular part of net baryonic density can to leading order be universally
expressed in terms of polylogarithms.
