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

TL;DR

This paper critically examines the claimed equivalence between bimodal energy distributions and zeros of the partition function in phase transition theory, showing that the relationship is more nuanced than previously suggested.

Contribution

It clarifies that zeros of the partition function can occur with both concave and nonconcave entropy functions, challenging prior assumptions about their association with first-order phase transitions.

Findings

Zeros of the partition function are not exclusively linked to nonconcave entropy functions.

Bimodal energy distributions are not a necessary condition for zeros of the partition function.

A detailed example demonstrates the subtlety in the relationship between zeros and entropy shape.

Abstract

I discuss the validity of a result put forward recently by Chomaz and Gulminelli [Physica A 330 (2003) 451] concerning the equivalence of two definitions of first-order phase transitions. I show that distributions of zeros of the partition function fulfilling the conditions of the Yang-Lee Theorem are not necessarily associated with nonconcave microcanonical entropy functions or, equivalently, with canonical distributions of the mean energy having a bimodal shape, as claimed by Chomaz and Gulminelli. In fact, such distributions of zeros can also be associated with concave entropy functions and unimodal canonical distributions having affine parts. A simple example is worked out in detail to illustrate this subtlety.