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Ralph Kenna's Scaling Relations in Critical Phenomena.

Leïla Moueddene^1,2,3, Arnaldo Donoso⁴, Bertrand Berche¹

¹Laboratoire de Physique et Chimie Théoriques, CNRS-Université de Lorraine, 54000 Nancy, France.

Entropy (Basel, Switzerland)

|March 28, 2024

Summary

This summary is machine-generated.

This study revisits scaling relations for critical exponents, proposing a new derivation and correcting a proposed scaling relation for correlation functions. The findings offer refined understanding in critical phenomena research.

Keywords:

critical exponents finite-size scaling logarithmic corrections scaling and renormalization scaling laws tricritical point

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Area of Science:

Statistical Physics
Critical Phenomena
Theoretical Physics

Background:

Scaling relations are crucial for understanding critical phenomena.
Previous work by Kenna, Johnston, and Janke established key relations among "hatted critical exponents".

Purpose of the Study:

To revisit and propose alternative derivations for established scaling relations among "hatted critical exponents" developed by Kenna, Johnston, and Janke.
To propose a corrected form for the scaling relation concerning the correlation function's behavior, identifying a potential error in prior work.

Main Methods:

Revisiting and re-deriving existing theoretical frameworks.
Proposing alternative mathematical formulations for specific scaling relations.
Analyzing the behavior of correlation functions within critical phenomena models.

Main Results:

An alternative derivation is presented for some "hatted critical exponents" scaling relations.
A revised scaling relation for the correlation function is proposed, addressing a suspected error in previous literature.

Conclusions:

The study offers a refined theoretical perspective on critical exponent scaling relations.
The proposed correction to the correlation function's scaling relation may enhance the accuracy of critical phenomena predictions.