Exact Correlation Function at the Lifshitz Points of the Spherical Model

TL;DR

This paper provides an exact calculation of the spin-spin correlation function at an anisotropic Lifshitz point in the spherical model, confirming universality and exploring directional correlation behaviors.

Contribution

It offers the first exact form of the correlation function at Lifshitz points of arbitrary order in the spherical model, validating scaling and universality.

Findings

Correlation function matches scaling predictions

Scaling function is universal across parameters

Directional correlations can switch between ferromagnetic and antiferromagnetic

Abstract

The spin-spin correlation function of the spherical model being precisely at an anisotropic Lifshitz point of arbitrary order is calculated exactly. The results are in agreement with scaling. The scaling function is shown to be universal. The direction-dependent long-range correlations may change from ferromagnetic to antiferromagnetic behaviour and back as the dimension is varied. The form of the scaling function is compared to predictions following from local scale invariance for strongly anisotropic critical systems.