Uniaxial Lifshitz Point at $O({\epsilon }_L^2)$

Abstract

The critical exponents ${\nu }_{L2},{\eta }_{L2}$ and ${\gamma }_{L2}$ of a uniaxial Lifshitz point are calculated at two-loop level using renormalization group and ${\epsilon }_L$-expansion techniques. We found a new constraint involving the loop momenta along the competition axis, which allows to solve the two-loop integrals. The exponent ${\gamma }_{L2}$ obtained using our method is in good agreement with numerical estimates based on Monte Carlo simulations.

18 pages, Revtex, updated version with four figures, some references added