Properties of Higher-Order Phase Transitions

TL;DR

This paper investigates higher-order phase transitions using partition function zeros, deriving properties, scaling relations, and presenting new insights into their potential existence in physical systems.

Contribution

It provides a theoretical analysis of higher-order phase transitions via partition function zeros, including new properties and scaling relations.

Findings

Derived properties of zero distributions for higher-order transitions

Recovered known scaling relations and introduced new ones

Highlighted the potential physical existence of higher-order transitions

Abstract

Experimental evidence for the existence of strictly higher-order phase transitions (of order three or above in the Ehrenfest sense) is tenuous at best. However, there is no known physical reason why such transitions should not exist in nature. Here, higher-order transitions characterized by both discontinuities and divergences are analysed through the medium of partition function zeros. Properties of the distributions of zeros are derived, certain scaling relations are recovered, and new ones are presented.