Susceptibility Amplitude Ratios Near a Lifshitz Point

TL;DR

This paper calculates the susceptibility amplitude ratio near a uniaxial Lifshitz point using field-theoretic methods and epsilon expansion, providing specific numerical results for cubic lattices.

Contribution

It introduces a new symmetry point for renormalization and computes the susceptibility amplitude ratio at one-loop level near a Lifshitz point.

Findings

Calculated ratio C+ / C- = 3.85 for cubic lattice (d=3).

Used Schwinger parametrization and epsilon expansion techniques.

Developed a new symmetry point for renormalization purposes.

Abstract

The susceptibility amplitude ratio in the neighborhood of a uniaxial Lifshitz point is calculated at one-loop level using field-theoretic and $\epsilon_{L}$-expansion methods. We use the Schwinger parametrization of the propagator in order to split the quadratic and quartic part of the momenta, as well as a new special symmetry point suitable for renormalization purposes. For a cubic lattice (d = 3), we find the result $\frac{C_{+}}{C_{-}} = 3.85$.