First order phase transitions: equivalence between bimodalities and the Yang-Lee theorem

TL;DR

This paper establishes a fundamental equivalence between bimodality in finite systems, thermodynamic potential curvature, and the Yang-Lee theorem, linking phase transition signatures across different frameworks.

Contribution

It demonstrates the one-to-one correspondence between bimodality, thermodynamic potential curvature, and Yang-Lee zeros in the thermodynamic limit.

Findings

Bimodality is equivalent to the inverted curvature of the thermodynamic potential.

Bimodality corresponds to the distribution of partition function zeros on a line in the complex plane.

The distribution of zeros scales with the number of particles.

Abstract

First order phase transitions in finite systems can be defined through the bimodality of the distribution of the order parameter. This definition is equivalent to the one based on the inverted curvature of the thermodynamic potential. Moreover we show that it is in a one to one correspondence with the Yang Lee theorem in the thermodynamic limit. Bimodality is a necessary and sufficient condition for zeroes of the partition sum in the control intensive variable complex plane to be distributed on a line perpendicular to the real axis with a uniform density, scaling like the number of particles.