Compatibility of 1/n and epsilon expansions for critical exponents at m-axial Lifshitz points

TL;DR

This paper demonstrates that large-n and epsilon expansions for critical exponents at m-axial Lifshitz points are compatible, showing consistency between two different theoretical approaches in critical phenomena analysis.

Contribution

It proves the compatibility of large-n and epsilon expansions for critical exponents at Lifshitz points, confirming their consistency up to second order in epsilon.

Findings

Large-n and epsilon expansions agree up to order epsilon^2/n.

Both methods yield identical contributions at second order in epsilon.

The results support the validity of using either expansion in critical phenomena studies.

Abstract

The critical behaviour of d-dimensional n-vector models at m-axial Lifshitz points is considered for general values of m in the large-n limit. It is proven that the recently obtained large-N expansions [J. Phys.: Condens. Matter 17, S1947 (2005)] of the correlation exponents \eta_{L2}, \eta_{L4} and the related anisotropy exponent \theta are fully consistent with the dimensionality expansions to second order in \epsilon=4+m/2-d [Phys. Rev. B 62, 12338 (2000); Nucl. Phys. B 612, 340 (2001)] inasmuch as both expansions yield the same contributions of order \epsilon^2/n.