Critical behavior at m-axial Lifshitz points: Field-theory analysis and epsilon-expansion results

The critical behavior of d-dimensional systems with an n-component order pa rameter is reconsidered at (m,d,n)-lifshitz points, where a wave-vector ins tability occurs in an m-dimensional subspace of R-d. Our aim is to sort out which ones of the previously published partly contradictory epsilon -expan sion results to second order in epsilon =4+ m/2-d are correct. To this end, a field-theory calculation is performed directly in the position space of d=4+m/2-epsilon dimensions, using dimensional regularization and minimal su btraction of ultraviolet poles. The residua of the dimensionally regularize d integrals that are required to determine the series expansions of the cor relation exponents eta (12), and eta (14) and of the wave-vector exponent b eta (q) to order epsilon (2) are reduced to single integrals, which for gen eral m= 1,...,d-1 can be computed numerically, and for special values of nt , analytically. Our results are at variance with the original predictions f or general m. For m = 2 and m = 6, we confirm the results of Sak and Grest [Phys. Rev. B 17, 3602 (1978)] and Mergulhao and Carneiro's recent held-the ory analysis [Phys. Rev. B 59, 13 954 (1999)].