Classification of phase transitions in small systems

TL;DR

This paper introduces a classification scheme for phase transitions in finite systems using Lee-Yang zeros, bridging finite and infinite system behaviors, and applies it to Bose-Einstein condensates and small argon clusters.

Contribution

It proposes a novel classification method for phase transitions in finite systems based on Lee-Yang zeros, connecting finite and thermodynamic limits.

Findings

The scheme reduces to Ehrenfest's definition in the infinite limit.

Applied to Bose-Einstein condensates, identifying higher order phase transitions.

Analyzed small argon clusters to classify their phase transition behavior.

Abstract

We present a classification scheme for phase transitions in finite systems like atomic and molecular clusters based on the Lee-Yang zeros in the complex temperature plane. In the limit of infinite particle numbers the scheme reduces to the Ehrenfest definition of phase transitions and gives the right critical indices. We apply this classification scheme to Bose-Einstein condensates in a harmonic trap as an example of a higher order phase transitions in a finite system and to small Ar clusters.