128 research outputs found
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
Reply to "Comment on Renormalization group picture of the Lifshitz critical behaviors"
We reply to a recent comment by Diehl and Shpot (cond-mat/0305131)
criticizing a new approach to the Lifshitz critical behavior just presented (M.
M. Leite Phys. Rev. B 67, 104415(2003)). We show that this approach is free of
inconsistencies in the ultraviolet regime. We recall that the orthogonal
approximation employed to solve arbitrary loop diagrams worked out at the
criticized paper even at three-loop level is consistent with homogeneity for
arbitrary loop momenta. We show that the criticism is incorrect.Comment: RevTex, 6 page
Dynamic surface scaling behavior of isotropic Heisenberg ferromagnets
The effects of free surfaces on the dynamic critical behavior of isotropic
Heisenberg ferromagnets are studied via phenomenological scaling theory,
field-theoretic renormalization group tools, and high-precision computer
simulations. An appropriate semi-infinite extension of the stochastic model J
is constructed, the boundary terms of the associated dynamic field theory are
identified, its renormalization in d <= 6 dimensions is clarified, and the
boundary conditions it satisfies are given. Scaling laws are derived which
relate the critical indices of the dynamic and static infrared singularities of
surface quantities to familiar static bulk and surface exponents. Accurate
computer-simulation data are presented for the dynamic surface structure
factor; these are in conformity with the predicted scaling behavior and could
be checked by appropriate scattering experiments.Comment: 9 pages, 2 figure
Analytic Solution of Emden-Fowler Equation and Critical Adsorption in Spherical Geometry
In the framework of mean-field theory the equation for the order-parameter
profile in a spherically-symmetric geometry at the bulk critical point reduces
to an Emden-Fowler problem. We obtain analytic solutions for the surface
universality class of extraordinary transitions in for a spherical shell,
which may serve as a starting point for a pertubative calculation. It is
demonstrated that the solution correctly reproduces the Fisher-de Gennes effect
in the limit of the parallel-plate geometry.Comment: (to be published in Z. Phys. B), 7 pages, 1 figure, uuencoded
postscript file, 8-9
Critical Casimir amplitudes for -component models with O(n)-symmetry breaking quadratic boundary terms
Euclidean -component theories whose Hamiltonians are O(n)
symmetric except for quadratic symmetry breaking boundary terms are studied in
films of thickness . The boundary terms imply the Robin boundary conditions
at the boundary
planes at and . Particular attention is paid
to the cases in which of the variables
take the special value corresponding to critical
enhancement while the remaining ones are subcritically enhanced. Under these
conditions, the semi-infinite system bounded by has a
multicritical point, called -special, at which an symmetric
critical surface phase coexists with the O(n) symmetric bulk phase, provided
is sufficiently large. The -dependent part of the reduced free energy
per area behaves as as at the bulk critical
point. The Casimir amplitudes are determined for small
in the general case where components are
critically enhanced at both boundary planes, components are
enhanced at one plane but satisfy asymptotic Dirichlet boundary conditions at
the respective other, and the remaining components satisfy asymptotic
Dirichlet boundary conditions at both . Whenever ,
these expansions involve integer and fractional powers with
(mod logarithms). Results to for general values of
, , and are used to estimate the
of 3D Heisenberg systems with surface spin anisotropies when , , and .Comment: Latex source file with 5 eps files; version with minor amendments and
corrected typo
Proton-Antiproton Annihilation into a Lambda_c-Antilambda_c Pair
The process p-pbar -> Lambda_c-Antilambda_c is investigated within the
handbag approach. It is shown that the dominant dynamical mechanism,
characterized by the partonic subprocess u-ubar -> c-cbar factorizes in the
sense that only the subprocess contains highly virtual partons, a gluon to
lowest order of perturbative QCD, while the hadronic matrix elements embody
only soft scales and can be parameterized in terms of helicity flip and
non-flip generalized parton distributions. Modelling these parton distributions
by overlaps of light-cone wave functions for the involved baryons we are able
to predict cross sections and spin correlation parameters for the process of
interest.Comment: 39 pages, 7 figures, problems with printout of figures resolved, Ref.
33 and referring sentences in section 4 change
Surface critical exponents at a uniaxial Lifshitz point
Using Monte Carlo techniques, the surface critical behaviour of
three-dimensional semi-infinite ANNNI models with different surface
orientations with respect to the axis of competing interactions is
investigated. Special attention is thereby paid to the surface criticality at
the bulk uniaxial Lifshitz point encountered in this model. The presented Monte
Carlo results show that the mean-field description of semi-infinite ANNNI
models is qualitatively correct. Lifshitz point surface critical exponents at
the ordinary transition are found to depend on the surface orientation. At the
special transition point, however, no clear dependency of the critical
exponents on the surface orientation is revealed. The values of the surface
critical exponents presented in this study are the first estimates available
beyond mean-field theory.Comment: 10 pages, 7 figures include
Massive Field-Theory Approach to Surface Critical Behavior in Three-Dimensional Systems
The massive field-theory approach for studying critical behavior in fixed
space dimensions is extended to systems with surfaces.This enables one to
study surface critical behavior directly in dimensions without having to
resort to the expansion. The approach is elaborated for the
representative case of the semi-infinite |\bbox{\phi}|^4 -vector model
with a boundary term {1/2} c_0\int_{\partial V}\bbox{\phi}^2 in the action.
To make the theory uv finite in bulk dimensions , a renormalization
of the surface enhancement is required in addition to the standard mass
renormalization. Adequate normalization conditions for the renormalized theory
are given. This theory involves two mass parameter: the usual bulk `mass'
(inverse correlation length) , and the renormalized surface enhancement .
Thus the surface renormalization factors depend on the renormalized coupling
constant and the ratio . The special and ordinary surface transitions
correspond to the limits with and ,
respectively. It is shown that the surface-enhancement renormalization turns
into an additive renormalization in the limit . The
renormalization factors and exponent functions with and
that are needed to determine the surface critical exponents of the special and
ordinary transitions are calculated to two-loop order. The associated series
expansions are analyzed by Pad\'e-Borel summation techniques. The resulting
numerical estimates for the surface critical exponents are in good agreement
with recent Monte Carlo simulations. This also holds for the surface crossover
exponent .Comment: Revtex, 40 pages, 3 figures, and 8 pictograms (included in equations
Relativistic Quantum Gravity at a Lifshitz Point
We show that the Horava theory for the completion of General Relativity at UV
scales can be interpreted as a gauge fixed theory, and it can be extended to an
invariant theory under the full group of four-dimensional diffeomorphisms. In
this respect, although being fully relativistic, it results to be locally
anisotropic in the time-like and space-like directions defined by a family of
irrotational observers. We show that this theory propagates generically three
degrees of freedom: two of them are related to the four-dimensional
diffeomorphism invariant graviton (the metric) and one is related to a
propagating scalar mode. Finally, we note that in the present formulation,
matter can be consistently coupled to gravity.Comment: v4: Erratum added: explanation on the true dynamical fields of the
relativistic theory added. The theory is interpreted as a Tensor-Scalar
relativistic theory. Reference added. Version accepted in JHE
Dynamical Relaxation and Universal Short-Time Behavior in Finite Systems: The Renormalization Group Approach
We study how the finite-sized n-component model A with periodic boundary
conditions relaxes near its bulk critical point from an initial nonequilibrium
state with short-range correlations. Particular attention is paid to the
universal long-time traces that the initial condition leaves. An approach based
on renormalization-group improved perturbation theory in 4-epsilon space
dimensions and a nonperturbative treatment of the q=0 mode of the fluctuating
order-parameter field is developed. This leads to a renormalized effective
stochastic equation for this mode in the background of the other q=0 modes; we
explicitly derive it to one-loop order, show that it takes the expected
finite-size scaling form at the fixed point, and solve it numerically. Our
results confirm for general n that the amplitude of the magnetization density
m(t) in the linear relaxation-time regime depends on the initial magnetization
in the universal fashion originally found in our large- analysis [J.\ Stat.
Phys. 73 (1993) 1]. The anomalous short-time power-law increase of m(t) also is
recovered. For n=1, our results are in fair agreement with recent Monte Carlo
simulations by Li, Ritschel, and Zheng [J. Phys. A 27 (1994) L837] for the
three-dimensional Ising model.Comment: 27 pages, 7 postscript figures, REVTEX 3.0, submitted to Nucl. Phys.
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