First-order phase transitions from poles in asymptotic representations of partition functions

Abstract

Although partition functions of finite-size systems are always analytic, and hence have no poles, they can be expressed in many cases as series containing terms with poles. Here we show that such poles can be related to linear branches of the entropy, expressed in the thermodynamic limit as a function of the energy per particle. We also show that these poles can be used to determine whether the entropy is nonconcave or has linear parts, which is something that cannot be done with the sole knowledge of the thermodynamic free energy derived from the partition function. We discuss applications for equilibrium systems having first-order phase transitions.

v1: 5 pages, RevTeX 4.1, 1 figure. v2: Typos corrected

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• Dynamical signatures of discontinuous phase transitions: How phase coexistence determines exponential versus power-law scaling
• Modified saddle-point integral near singularity for the large deviation function
• Large deviations for correlated random variables described by a matrix product ansatz
• Nonanalytic Landau functionals shaping the finite-size scaling of fluctuations and response functions in and out of equilibrium
• Ensemble Equivalence for Counterion Condensation on a Two Dimensional Charged Disc