Specific heat amplitude ratios for anisotropic Lifshitz critical behaviors

TL;DR

This paper calculates the universal specific heat amplitude ratio near a Lifshitz point using renormalization group methods, providing theoretical predictions that match experimental data for magnetic materials.

Contribution

It introduces a new field-theoretical $ ext{epsilon}_L$-expansion approach to determine the amplitude ratio at Lifshitz points, extending previous methods.

Findings

Calculated the amplitude ratio at one-loop order for $m=1$, $d=3$

Numerical estimate agrees with experimental data on $MnP$

Shows the ratio reduces to Ising case as $m o 0$

Abstract

We determine the specific heat amplitude ratio near a $m$-axial Lifshitz point and show its universal character. Using a recent renormalization group picture along with new field-theoretical $\epsilon_{L}$-expansion techniques, we established this amplitude ratio at one-loop order. We estimate the numerical value of this amplitude ratio for $m=1$ and $d=3$. The result is in very good agreement with its experimental measurement on the magnetic material $MnP$. It is shown that in the limit $m \to 0$ it trivially reduces to the Ising-like amplitude ratio.