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

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

2009-12-18

arxiv.org/abs/0912.3679v2

Phys. Rev. E 81, 030101(R) (1-4), 2010

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevE.81.030101

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.

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