Behaviour of the critical wavevector near a Lifshitz point

Abstract

Using scaling arguments, it is shown that, at a Lifshitz point, the exponent beta k is related to the crossover exponent phi by beta kappa= nu l4/ phi . The exponents eta l4 and beta kappa are calculated for a uniaxial Lifshitz point to O( epsilon l2), where epsilon l=4.5-d. The results are eta l4=-((n+2)/4(n+8)2) epsilon l2 and beta kappa=1/2+(7(n+2)/16(n+8)2) epsilon l2.