Abstract
The critical behavior of d-dimensional systems with an n-component order parameter is reconsidered at (m,d,n)-Lifshitz points, where a wave-vector instability occurs in an m-dimensional subspace of Our aim is to sort out which ones of the previously published partly contradictory ε-expansion results to second order in are correct. To this end, a field-theory calculation is performed directly in the position space of dimensions, using dimensional regularization and minimal subtraction of ultraviolet poles. The residua of the dimensionally regularized integrals that are required to determine the series expansions of the correlation exponents and and of the wave-vector exponent to order are reduced to single integrals, which for general can be computed numerically, and for special values of m, analytically. Our results are at variance with the original predictions for general m. For and we confirm the results of Sak and Grest [Phys. Rev. B 17, 3602 (1978)] and Mergulhão and Carneiro’s recent field-theory analysis [Phys. Rev. B 59, 13 954 (1999)].
- Received 30 May 2000
DOI:https://doi.org/10.1103/PhysRevB.62.12338
©2000 American Physical Society