A global analytic critical equations of state

TL;DR

This paper introduces a universal analytic form for equations of state that accurately captures critical behavior and challenges previous beliefs about the dependence of scaling fields.

Contribution

It presents a novel global analytic equation of state ensuring correct critical universality and scaling, and refutes prior assumptions about the dependence of scaling fields.

Findings

The proposed equations guarantee correct critical scaling behavior.

It demonstrates that the dependent scaling field can be explicitly expressed without singularities.

Challenges the traditional view on the dependence of scaling fields.

Abstract

We propose a general form for global analytic equations of state for which close to critical points, the correct universality and scaling behavior is guaranteed. A consequence of the construction is that the generally accepted belief that the dependent scaling field cannot be written as an explicit function of the relevant scaling fields without causing strongly singular behavior of the thermodynamic potential in the one-phase region, while in agreement with the state of the art in the past, is no longer correct.