Scaling laws at the critical point

TL;DR

This paper highlights the importance of a second critical exponent, η', which governs the decay of the fourth-order correlation function at critical points, linking it to thermodynamic behavior.

Contribution

It introduces and emphasizes the significance of the second independent exponent η' at critical points, connecting it to thermodynamic fluctuations and proposing a new scaling law.

Findings

Identification of a second critical exponent η'

Relation of η' to thermodynamic fluctuation-response

Proposal of a scaling law for η'

Abstract

There are two independent critical exponents that describe the behavior of systems near their critical point. However, at the critical point only the exponent $\eta$, which describes the decay of the correlation function, is usually discussed. We emphasize that there is a second independent exponent $\eta'$ that describes the decay of the fourth-order correlation function. The exponent $\eta'$ is related to the exponents determining the behavior of thermodynamic functions near criticality via a fluctuation-response equation for the specific heat. We also discuss a scaling law for $\eta'$.