16 research outputs found
Critical behavior at m-axial Lifshitz points: field-theory analysis and -expansion results
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
-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 m=1,...,d-1 can be computed numerically, and for
special values of m, analytically. Our results are at variance with the
original predictions for general m. For m=2 and m=6, we confirm the results of
Sak and Grest [Phys. Rev. B {\bf 17}, 3602 (1978)] and Mergulh{\~a}o and
Carneiro's recent field-theory analysis [Phys. Rev. B {\bf 59},13954 (1999)].Comment: Latex file with one figure (eps-file). Latex file uses texdraw to
generate figures that are included in the tex