Uniaxial Lifshitz Point at $O(ε_L^2)$

Abstract

The critical exponents $ν_{L2}, η_{L2}$ and $γ_{L2}$ of a uniaxial Lifshitz point are calculated at two-loop level using renormalization group and $ε_{L}$-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 $γ_{L2}$ obtained using our method is in good agreement with numerical estimates based on Monte Carlo simulations.