Exponent 1/4 from the mean field approximation

TL;DR

This paper investigates the magnetization behavior of a 3D ferromagnet near critical temperature using mean field approximation, revealing that in certain directions, the critical exponent is 1/4 instead of the typical 1/2.

Contribution

It demonstrates that the critical exponent for magnetization can be 1/4 in specific directions, challenging the usual mean field result.

Findings

Critical exponent is 1/4 in some directions near critical temperature.

Standard mean field exponent of 1/2 is not universal in all directions.

Directional dependence of magnetization exponent is identified.

Abstract

We consider the magnetization of the three-dimensional ferromagnetic near the critical temperature in the mean field approximation. It is found that for some directions of easy magnetization one obtains exponent 1/4 instead of the usual 1/2.