The analytic structure of thermodynamic systems with repulsive interactions

Abstract

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.

arXiv comment11 pages, 4 figures

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• Second order cumulants of conserved charge fluctuations revisited I. Vanishing chemical potentials
• Particlization of an interacting hadron resonance gas with global conservation laws for event-by-event fluctuations in heavy-ion collisions
• Traces of the nuclear liquid-gas phase transition in the analytic properties of hot QCD
• Critical point signatures in the cluster expansion in fugacities
• Constraining the hadronic spectrum and repulsive interactions in a hadron resonance gas via fluctuations of conserved charges
• From steady-state TASEP model with open boundaries to 1D Ising model at negative fugacity
• Net-Baryon Number Probability Distribution As an Indicator of Phase Transition