Browsing by Author "Shpot, M. A."
Now showing 1 - 2 of 2
Results Per Page
Sort Options
- Critical behavior at m-axial Lifshitz points: Field-theory analysis and epsilon-expansion resultsDiehl, H. W.; Shpot, M. A. (American Physical Society, 2000-11)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 R-d. Our aim is to sort out which ones of the previously published partly contradictory epsilon -expansion 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 subtraction of ultraviolet poles. The residua of the dimensionally regularized integrals that are required to determine the series expansions of the correlation exponents eta (12), and eta (14) and of the wave-vector exponent beta (q) to order epsilon (2) are reduced to single integrals, which for general m= 1,...,d-1 can be computed numerically, and for special values of nt, 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 Mergulhao and Carneiro's recent held-theory analysis [Phys. Rev. B 59, 13 954 (1999)].
- Relevance of space anisotropy in the critical behavior of m-axial Lifshitz pointsDiehl, H. W.; Shpot, M. A.; Zia, Royce K. P. (American Physical Society, 2003-12)The critical behavior of d-dimensional systems with n-component order parameter phi is studied at an m-axial Lifshitz point where a wave-vector instability occurs in an m-dimensional subspace R-m (m>1). Field theoretic renormalization group techniques are exploited to examine the effects of terms in the Hamiltonian that break the rotational symmetry of the Euclidean group E(m). The framework for considering general operators of second order in phi and fourth order in the derivatives partial derivative(alpha) with respect to the Cartesian coordinates x(alpha) of R-m is presented. For the specific case of systems with cubic anisotropy, the effects of having an additional term, Sigma(alpha=1)(m)(partial derivative(alpha)(2)phi)(2), are investigated in an epsilon expansion about the upper critical dimension d(*)(m)=4+m/2. Its associated crossover exponent is computed to order epsilon(2) and found to be positive, so that it is a relevant perturbation on a model isotropic in R-m.