12 research outputs found
Susceptibility Amplitude Ratios Near a Lifshitz Point
The susceptibility amplitude ratio in the neighborhood of a uniaxial Lifshitz
point is calculated at one-loop level using field-theoretic and
-expansion methods. We use the Schwinger parametrization of the
propagator in order to split the quadratic and quartic part of the momenta, as
well as a new special symmetry point suitable for renormalization purposes. For
a cubic lattice (d = 3), we find the result .Comment: 7 pages, late
A new picture of the Lifshitz critical behavior
New field theoretic renormalization group methods are developed to describe
in a unified fashion the critical exponents of an m-fold Lifshitz point at the
two-loop order in the anisotropic (m not equal to d) and isotropic (m=d close
to 8) situations. The general theory is illustrated for the N-vector phi^4
model describing a d-dimensional system. A new regularization and
renormalization procedure is presented for both types of Lifshitz behavior. The
anisotropic cases are formulated with two independent renormalization group
transformations. The description of the isotropic behavior requires only one
type of renormalization group transformation. We point out the conceptual
advantages implicit in this picture and show how this framework is related to
other previous renormalization group treatments for the Lifshitz problem. The
Feynman diagrams of arbitrary loop-order can be performed analytically provided
these integrals are considered to be homogeneous functions of the external
momenta scales. The anisotropic universality class (N,d,m) reduces easily to
the Ising-like (N,d) when m=0. We show that the isotropic universality class
(N,m) when m is close to 8 cannot be obtained from the anisotropic one in the
limit d --> m near 8. The exponents for the uniaxial case d=3, N=m=1 are in
good agreement with recent Monte Carlo simulations for the ANNNI model.Comment: 48 pages, no figures, two typos fixe
Boundary critical behavior at m-axial Lifshitz points for a boundary plane parallel to the modulation axes
The critical behavior of semi-infinite -dimensional systems with
-component order parameter and short-range interactions is
investigated at an -axial bulk Lifshitz point whose wave-vector instability
is isotropic in an -dimensional subspace of . The associated
modulation axes are presumed to be parallel to the surface, where . An appropriate semi-infinite model representing the
corresponding universality classes of surface critical behavior is introduced.
It is shown that the usual O(n) symmetric boundary term
of the Hamiltonian must be supplemented by one of the form involving a
dimensionless (renormalized) coupling constant . The implied boundary
conditions are given, and the general form of the field-theoretic
renormalization of the model below the upper critical dimension
is clarified. Fixed points describing the ordinary, special,
and extraordinary transitions are identified and shown to be located at a
nontrivial value if . The surface
critical exponents of the ordinary transition are determined to second order in
. Extrapolations of these expansions yield values of these
exponents for in good agreement with recent Monte Carlo results for the
case of a uniaxial () Lifshitz point. The scaling dimension of the surface
energy density is shown to be given exactly by , where
is the anisotropy exponent.Comment: revtex4, 31 pages with eps-files for figures, uses texdraw to
generate some graphs; to appear in PRB; v2: some references and additional
remarks added, labeling in figure 1 and some typos correcte
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
Susceptibility amplitude ratio for generic competing systems
We calculate the susceptibility amplitude ratio near a generic higher
character Lifshitz point up to one-loop order. We employ a renormalization
group treatment with independent scaling transformations associated to the
various inequivalent subspaces in the anisotropic case in order to compute the
ratio above and below the critical temperature and demonstrate its
universality. Furthermore, the isotropic results with only one type of
competition axes have also been shown to be universal. We describe how the
simpler situations of -axial Lifshitz points as well as ordinary
(noncompeting) systems can be retrieved from the present framework.Comment: 20 pages, no figure
Anomalous dimensions and phase transitions in superconductors
The anomalous scaling in the Ginzburg-Landau model for the superconducting
phase transition is studied. It is argued that the negative sign of the
exponent is a consequence of a special singular behavior in momentum space. The
negative sign of comes from the divergence of the critical correlation
function at finite distances. This behavior implies the existence of a Lifshitz
point in the phase diagram. The anomalous scaling of the vector potential is
also discussed. It is shown that the anomalous dimension of the vector
potential has important consequences for the critical dynamics in
superconductors. The frequency-dependent conductivity is shown to obey the
scaling . The prediction is
obtained from existing Monte Carlo data.Comment: RevTex, 20 pages, no figures; small changes; version accepted in PR
A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)
Meeting abstrac