8,165 research outputs found
Boundary critical behaviour at -axial Lifshitz points: the special transition for the case of a surface plane parallel to the modulation axes
The critical behaviour of -dimensional semi-infinite systems with
-component order parameter is studied at an -axial bulk
Lifshitz point whose wave-vector instability is isotropic in an -dimensional
subspace of . Field-theoretic renormalization group methods are
utilised to examine the special surface transition in the case where the
potential modulation axes, with , are parallel to the surface.
The resulting scaling laws for the surface critical indices are given. The
surface critical exponent , the surface crossover exponent
and related ones are determined to first order in
\epsilon=4+\case{m}{2}-d. Unlike the bulk critical exponents and the surface
critical exponents of the ordinary transition, is -dependent already
at first order in . The \Or(\epsilon) term of is
found to vanish, which implies that the difference of and
the bulk exponent is of order .Comment: 21 pages, one figure included as eps file, uses IOP style file
Critical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order
A two-loop renormalization group analysis of the critical behaviour at an
isotropic Lifshitz point is presented. Using dimensional regularization and
minimal subtraction of poles, we obtain the expansions of the critical
exponents and , the crossover exponent , as well as the
(related) wave-vector exponent , and the correction-to-scaling
exponent to second order in . These are compared with
the authors' recent -expansion results [{\it Phys. Rev. B} {\bf 62}
(2000) 12338; {\it Nucl. Phys. B} {\bf 612} (2001) 340] for the general case of
an -axial Lifshitz point. It is shown that the expansions obtained here by a
direct calculation for the isotropic () Lifshitz point all follow from the
latter upon setting . This is so despite recent claims to the
contrary by de Albuquerque and Leite [{\it J. Phys. A} {\bf 35} (2002) 1807].Comment: 11 pages, Latex, uses iop stylefiles, some graphs are generated
automatically via texdra
Renormalized field theory and particle density profile in driven diffusive systems with open boundaries
We investigate the density profile in a driven diffusive system caused by a
plane particle source perpendicular to the driving force. Focussing on the case
of critical bulk density we use a field theoretic renormalization
group approach to calculate the density as a function of the distance
from the particle source at first order in (: spatial
dimension). For we find reasonable agreement with the exact solution
recently obtained for the asymmetric exclusion model. Logarithmic corrections
to the mean field profile are computed for with the result for .Comment: 32 pages, RevTex, 4 Postscript figures, to appear in Phys. Rev.
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
Lifshitz-point critical behaviour to
We comment on a recent letter by L. C. de Albuquerque and M. M.
Leite (J. Phys. A: Math. Gen. 34 (2001) L327-L332), in which results to
second order in were presented for the critical
exponents , and
of d-dimensional systems at m-axial Lifshitz points.
We point out that their results are at variance with ours. The discrepancy is
due to their incorrect computation of momentum-space integrals. Their
speculation that the field-theoretic renormalization group approach, if
performed in position space, might give results different from when it is
performed in momentum space is refuted.Comment: Latex file, uses the included iop stylefiles; Uses the texdraw
package to generate included figure
Surface critical behavior of driven diffusive systems with open boundaries
Using field theoretic renormalization group methods we study the critical
behavior of a driven diffusive system near a boundary perpendicular to the
driving force. The boundary acts as a particle reservoir which is necessary to
maintain the critical particle density in the bulk. The scaling behavior of
correlation and response functions is governed by a new exponent eta_1 which is
related to the anomalous scaling dimension of the chemical potential of the
boundary. The new exponent and a universal amplitude ratio for the density
profile are calculated at first order in epsilon = 5-d. Some of our results are
checked by computer simulations.Comment: 10 pages ReVTeX, 6 figures include
Effects of surfaces on resistor percolation
We study the effects of surfaces on resistor percolation at the instance of a
semi-infinite geometry. Particularly we are interested in the average
resistance between two connected ports located on the surface. Based on general
grounds as symmetries and relevance we introduce a field theoretic Hamiltonian
for semi-infinite random resistor networks. We show that the surface
contributes to the average resistance only in terms of corrections to scaling.
These corrections are governed by surface resistance exponents. We carry out
renormalization group improved perturbation calculations for the special and
the ordinary transition. We calculate the surface resistance exponents
\phi_{\mathcal S \mathnormal} and \phi_{\mathcal S \mathnormal}^\infty for
the special and the ordinary transition, respectively, to one-loop order.Comment: 19 pages, 3 figure
Comment on `Renormalization-Group Calculation of the Dependence on Gravity of the Surface Tension and Bending Rigidity of a Fluid Interface'
It is shown that the interface model introduced in Phys. Rev. Lett. 86, 2369
(2001) violates fundamental symmetry requirements for vanishing gravitational
acceleration , so that its results cannot be applied to critical properties
of interfaces for .Comment: A Comment on a recent Letter by J.G. Segovia-L\'opez and V.
Romero-Roch\'{\i}n, Phys. Rev. Lett.86, 2369 (2001). Latex file, 1 page
(revtex
Development of an improved oxygen electrode for use in alkaline H2-O2 fuel cells Quarterly report, Apr. 1 - Jun. 30, 1967
Preparation of institial compounds of transition metals for hydrogen oxygen fuel cell cathode
Large-n expansion for m-axial Lifshitz points
The large-n expansion is developed for the study of critical behaviour of
d-dimensional systems at m-axial Lifshitz points with an arbitrary number m of
modulation axes. The leading non-trivial contributions of O(1/n) are derived
for the two independent correlation exponents \eta_{L2} and \eta_{L4}, and the
related anisotropy index \theta. The series coefficients of these 1/n
corrections are given for general values of m and d with 0<m<d and
2+m/2<d<4+m/2 in the form of integrals. For special values of m and d such as
(m,d)=(1,4), they can be computed analytically, but in general their evaluation
requires numerical means. The 1/n corrections are shown to reduce in the
appropriate limits to those of known large-n expansions for the case of
d-dimensional isotropic Lifshitz points and critical points, respectively, and
to be in conformity with available dimensionality expansions about the upper
and lower critical dimensions. Numerical results for the 1/n coefficients of
\eta_{L2}, \eta_{L4} and \theta are presented for the physically interesting
case of a uniaxial Lifshitz point in three dimensions, as well as for some
other choices of m and d. A universal coefficient associated with the
energy-density pair correlation function is calculated to leading order in 1/n
for general values of m and d.Comment: 28 pages, 3 figures. Submitted to: J. Phys. C: Solid State Phys.,
special issue dedicated to Lothar Schaefer on the occasion of his 60th
birthday. V2: References added along with corresponding modifications in the
text, corrected figure 3, corrected typo
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