Susceptibility amplitude ratio for generic competing systems

TL;DR

This paper computes the susceptibility amplitude ratio near a Lifshitz point using renormalization group methods, demonstrating its universality across various anisotropic and isotropic systems.

Contribution

It introduces a unified framework to calculate the susceptibility amplitude ratio for generic Lifshitz points, including anisotropic and isotropic cases, showing their universal behavior.

Findings

The susceptibility amplitude ratio is universal near Lifshitz points.

The framework applies to both anisotropic and isotropic systems.

Simpler cases like m-axial Lifshitz points are recoverable from the general model.

Abstract

We calculate the susceptibility amplitude ratio near a generic higher character Lifshitz point up to one-loop order. We employ a renormalization group treatment with $L$ independent scaling transformations associated to the various inequivalent subspaces in the anisotropic case in order to compute the ratio above and below the critical temperature and demonstrate its universality. Furthermore, the isotropic results with only one type of competition axes have also been shown to be universal. We describe how the simpler situations of $m$-axial Lifshitz points as well as ordinary (noncompeting) systems can be retrieved from the present framework.