Properties of phase transitions of higher order

TL;DR

This paper investigates higher-order phase transitions using partition function zeros, deriving distribution results and scaling relations, highlighting their theoretical existence despite limited experimental evidence.

Contribution

It introduces a framework for analyzing higher-order phase transitions via partition function zeros, providing new insights into their distribution and critical scaling behavior.

Findings

Distribution of zeros for higher-order transitions derived

Scaling relations between critical exponents established

Supports the theoretical plausibility of higher-order transitions

Abstract

There is only limited experimental evidence for the existence in nature of phase transitions of Ehrenfest order greater than two. However, there is no physical reason for their non-existence, and such transitions certainly exist in a number of theoretical models in statistical physics and lattice field theory. Here, higher-order transitions are analysed through the medium of partition function zeros. Results concerning the distributions of zeros are derived as are scaling relations between some of the critical exponents.