Singularities in Free Energy: Lee-Yang Theory

TL;DR

This paper discusses Lee-Yang theory, which links phase transitions to singularities in free energy and explores complex roots of the partition function, including multi-phase coexistence and comparisons to Mayer's theory.

Contribution

It provides an analysis of singularities in free energy related to phase transitions, extending to multi-phase systems and comparing with Mayer's theory.

Findings

Singularities of free energy are associated with phase transitions.

Complex roots of the partition function indicate phase coexistence.

Extended discussion on multi-phase systems and comparison with Mayer's theory.

Abstract

Phase Transition is associated with a drastic change in some observable (ordered parameter) of the system when the controlled parameter is tuned smoothly. Lee-Yang theory of phase transition is discussed which is related to the accumulation of singularities of free energy, equivalently complex roots of Grand Partition function (Partition function) at points on positive real axis in complex fugacity plane; and more general (p+1) phase system is discussed, and also the case when (w+2) phases coexist together. Comparison to Mayer's theory is also presented.