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

H. W. Diehl and M. Shpot
Phys. Rev. B 62, 12338 – Published 1 November 2000
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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 Rd. Our aim is to sort out which ones of the previously published partly contradictory ε-expansion results to second order in ε=4+m/2d are correct. To this end, a field-theory calculation is performed directly in the position space of d=4+m/2ε 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 ηl2 and ηl4 and of the wave-vector exponent βq to order ε2 are reduced to single integrals, which for general m=1,,d1 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 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

Authors & Affiliations

H. W. Diehl

  • Fachbereich Physik, Universität-Gesamthochschule Essen, D-45117 Essen, Federal Republic of Germany
  • Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24601

M. Shpot*

  • Fachbereich Physik, Universität-Gesamthochschule Essen, D-45117 Essen, Federal Republic of Germany

  • *Permanent address: Institute for Condensed Matter Physics, 1 Svientsitskii str., 79011 Lviv, Ukraine. Email address: shpot@theo-phys.uni-essen.de

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Vol. 62, Iss. 18 — 1 November 2000

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