484 research outputs found
Critical behavior of three-dimensional magnets with complicated ordering from three-loop renormalization-group expansions
The critical behavior of a model describing phase transitions in 3D
antiferromagnets with 2N-component real order parameters is studied within the
renormalization-group (RG) approach. The RG functions are calculated in the
three-loop order and resummed by the generalized Pade-Borel procedure
preserving the specific symmetry properties of the model. An anisotropic stable
fixed point is found to exist in the RG flow diagram for N > 1 and lies near
the Bose fixed point; corresponding critical exponents are close to those of
the XY model. The accuracy of the results obtained is discussed and estimated.Comment: 10 pages, LaTeX, revised version published in Phys. Rev.
On stability of the three-dimensional fixed point in a model with three coupling constants from the expansion: Three-loop results
The structure of the renormalization-group flows in a model with three
quartic coupling constants is studied within the -expansion method up
to three-loop order. Twofold degeneracy of the eigenvalue exponents for the
three-dimensionally stable fixed point is observed and the possibility for
powers in to appear in the series is investigated.
Reliability and effectiveness of the -expansion method for the given
model is discussed.Comment: 14 pages, LaTeX, no figures. To be published in Phys. Rev. B, V.57
(1998
Theory of optical spectra of polar quantum wells: Temperature effects
Theoretical and numerical calculations of the optical absorption spectra of
excitons interacting with longitudinal-optical phonons in quasi-2D polar
semiconductors are presented. In II-VI semiconductor quantum wells, exciton
binding energy can be tuned on- and off-resonance with the longitudinal-optical
phonon energy by varying the quantum well width. A comprehensive picture of
this tunning effect on the temperature-dependent exciton absorption spectrum is
derived, using the exciton Green's function formalism at finite temperature.
The effective exciton-phonon interaction is included in the Bethe-Salpeter
equation. Numerical results are illustrated for ZnSe-based quantum wells. At
low temperatures, both a single exciton peak as well as a continuum resonance
state are found in the optical absorption spectra. By contrast, at high enough
temperatures, a splitting of the exciton line due to the real phonon absorption
processes is predicted. Possible previous experimental observations of this
splitting are discussed.Comment: 10 pages, 9 figures, to appear in Phys. Rev. B. Permanent address:
[email protected]
On critical behavior of phase transitions in certain antiferromagnets with complicated ordering
Within the four-loop \ve expansion, we study the critical behavior of
certain antiferromagnets with complicated ordering. We show that an anisotropic
stable fixed point governs the phase transitions with new critical exponents.
This is supported by the estimate of critical dimensionality
obtained from six loops via the exact relation established
for the real and complex hypercubic models.Comment: Published versio
Non-Fermi liquid behavior from two-dimensional antiferromagnetic fluctuations: a renormalization-group and large-N analysis
We analyze the Hertz-Moriya-Millis theory of an antiferromagnetic quantum
critical point, in the marginal case of two dimensions (d=2,z=2). Up to
next-to-leading order in the number of components (N) of the field, we find
that logarithmic corrections do not lead to an enhancement of the Landau
damping. This is in agreement with a renormalization-group analysis, for
arbitrary N. Hence, the logarithmic effects are unable to account for the
behavior reportedly observed in inelastic neutron scattering experiments on
CeCu_{6-x}Au_x. We also examine the extended dynamical mean-field treatment
(local approximation) of this theory, and find that only subdominant
corrections to the Landau damping are obtained within this approximation, in
contrast to recent claims.Comment: 15 pages, 8 figure
Mars Sample Return: The Value of Depth Profiles
Sample return from Mars offers the promise of data from Martian materials that have previously only been available from meteorites. Return of carefully selected samples may yield more information about the history of water and possible habitability through Martian history. Here we propose that samples collected from Mars should include depth profiles of material across the interface between weathered material on the surface of Mars into unweathered parent rock material. Such profiles have the potential to yield chemical kinetic data that can be used to estimate the duration of water and information about potential habitats on Mars
Driven diffusive system with non-local perturbations
We investigate the impact of non-local perturbations on driven diffusive
systems. Two different problems are considered here. In one case, we introduce
a non-local particle conservation along the direction of the drive and in
another case, we incorporate a long-range temporal correlation in the noise
present in the equation of motion. The effect of these perturbations on the
anisotropy exponent or on the scaling of the two-point correlation function is
studied using renormalization group analysis.Comment: 11 pages, 2 figure
Two-dimensional SIR epidemics with long range infection
We extend a recent study of susceptible-infected-removed epidemic processes
with long range infection (referred to as I in the following) from
1-dimensional lattices to lattices in two dimensions. As in I we use hashing to
simulate very large lattices for which finite size effects can be neglected, in
spite of the assumed power law for the
probability that a site can infect another site a distance vector
apart. As in I we present detailed results for the critical case, for the
supercritical case with , and for the supercritical case with . For the latter we verify the stretched exponential growth of the
infected cluster with time predicted by M. Biskup. For we find
generic power laws with dependent exponents in the supercritical
phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead
of diverging exponentially with the distance from the critical point, the
correlation length increases with an inverse power, as in an ordinary critical
point. Finally we study the dependence of the critical exponents on in
the regime , and compare with field theoretic predictions. In
particular we discuss in detail whether the critical behavior for
slightly less than 2 is in the short range universality class, as conjectured
recently by F. Linder {\it et al.}. As in I we also consider a modified version
of the model where only some of the contacts are long range, the others being
between nearest neighbors. If the number of the latter reaches the percolation
threshold, the critical behavior is changed but the supercritical behavior
stays qualitatively the same.Comment: 14 pages, including 29 figure
Randomly dilute spin models with cubic symmetry
We study the combined effect of cubic anisotropy and quenched uncorrelated
impurities on multicomponent spin models. For this purpose, we consider the
field-theoretical approach based on the Ginzburg-Landau-Wilson
Hamiltonian with cubic-symmetric quartic interactions and quenched randomness
coupled to the local energy density. We compute the renormalization-group
functions to six loops in the fixed-dimension (d=3) perturbative scheme. The
analysis of such high-order series provides an accurate description of the
renormalization-group flow. The results are also used to determine the critical
behavior of three-dimensional antiferromagnetic three- and four-state Potts
models in the presence of quenched impurities.Comment: 23 pages, 1 figure
Random Walks with Long-Range Self-Repulsion on Proper Time
We introduce a model of self-repelling random walks where the short-range
interaction between two elements of the chain decreases as a power of the
difference in proper time. Analytic results on the exponent are obtained.
They are in good agreement with Monte Carlo simulations in two dimensions. A
numerical study of the scaling functions and of the efficiency of the algorithm
is also presented.Comment: 25 pages latex, 4 postscript figures, uses epsf.sty (all included)
IFUP-Th 13/92 and SNS 14/9
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