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

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

2012-02-11

arxiv.org/abs/1202.2464v2

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, submitted to Nucl. Phys. B. V2 - journal version with an extended introduction containing a short review of both Lif

Scientific paper

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.

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