Lifshitz-point correlation length exponents from the large-n expansion
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.
Cite
@article{arxiv.1202.2464,
title = {Lifshitz-point correlation length exponents from the large-n expansion},
author = {M. A. Shpot and Yu. M. Pis'mak},
journal= {arXiv preprint arXiv:1202.2464},
year = {2012}
}
Comments
27 pages, submitted to Nucl. Phys. B. V2 - journal version with an extended introduction containing a short review of both Lifshitz-point and Lorentz-violating theories