An Assumption About The Free Energy Near The Critical Point

TL;DR

This paper proposes a new assumed form for the singular part of free energy near the critical point, deriving scaling laws and critical exponents that differ from Widom's hypothesis, aiming to guide future research.

Contribution

It introduces a novel assumption about the singular part of free energy near critical points, leading to new scaling laws and critical exponents.

Findings

Derives critical exponents from the new singular free energy form

Shows the form satisfies Widom's scaling function qualities

Provides a basis for future theoretical research in critical phenomena

Abstract

We divide the free energy near the critical point into two parts. One is the regular part, the other is the singular part. The singular part is assumed to be a concrete possible form. The singular part in this form is different from Widom scaling hypothesis and can give out the scaling laws of the critical exponents about the thermodynamic quantities. Furthermore, the critical exponents will be right worked out. We proof the singular part in this form can satisfy the qualities of the scaling function mentioned out by Widom. As an assumption, we expect the free energy in this form will be significative for the future research. Note: If you have any suggestions when this paper is considered, connect us with E-mail:lanmanhuayu@yahoo.com.cn, please.:)