Lifshitz-point correlation length exponents from the large-n expansion

TL;DR

This paper uses the large-n expansion method to calculate critical exponents at Lifshitz points, providing analytical and numerical results that align with known theories and extend understanding of anisotropic critical phenomena.

Contribution

It derives the leading 1/n correction for the perpendicular correlation-length exponent at Lifshitz points, extending large-n expansion results to anisotropic systems.

Findings

Derived 1/n correction for nu_{L2} exponent.

Results consistent with known large-n and epsilon expansions.

Numerical estimates for d=3, m=1, n=3.

Abstract

The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m-axial Lifshitz points. We derive the leading nontrivial 1/n correction for the perpendicular correlation-length exponent nu_{L2} and hence several related thermal exponents to order O(1/n). The results are consistent with known large-n expansions for d-dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d^*=4+m/2 for generic m\in[0,d]. Analytical results are given for the special case d=4, m=1. For uniaxial Lifshitz points in three dimensions, 1/n coefficients are calculated numerically. The estimates of critical exponents at d=3, m=1 and n=3 are discussed.