2,629 research outputs found
Helmholtz decomposition theorem and Blumenthal's extension by regularization
Helmholtz decomposition theorem for vector fields is usually presented with
too strong restrictions on the fields and only for time independent fields.
Blumenthal showed in 1905 that decomposition is possible for any asymptotically
weakly decreasing vector field. He used a regularization method in his proof
which can be extended to prove the theorem even for vector fields
asymptotically increasing sublinearly. Blumenthal's result is then applied to
the time-dependent fields of the dipole radiation and an artificial sublinearly
increasing field.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1506.0023
Biconical critical dynamics
A complete two loop renormalization group calculation of the multicritical
dynamics at a tetracritical or bicritical point in anisotropic antiferromagnets
in an external magnetic field is performed. Although strong scaling for the two
order parameters (OPs) perpendicular and parallel to the field is restored as
found earlier, in the experimentally accessible region the effective dynamical
exponents for the relaxation of the OPs remain different since their equal
asymptotic values are not reached.Comment: 6 pages, 2 figures; some additions, corrected typo
Phase Transition in the Random Anisotropy Model
The influence of a local anisotropy of random orientation on a ferromagnetic
phase transition is studied for two cases of anisotropy axis distribution. To
this end a model of a random anisotropy magnet is analyzed by means of the
field theoretical renormalization group approach in two loop approximation
refined by a resummation of the asymptotic series. The one-loop result of
Aharony indicating the absence of a second-order phase transition for an
isotropic distribution of random anisotropy axis at space dimension is
corroborated. For a cubic distribution the accessible stable fixed point leads
to disordered Ising-like critical exponents.Comment: 10 pages, 2 latex figures and a style file include
Critical light scattering in liquids
We compare theoretical results for the characteristic frequency of the
Rayleigh peak calculated in one-loop order within the field theoretical method
of the renormalization group theory with experiments and other theoretical
results. Our expressions describe the non-asymptotic crossover in temperature,
density and wave vector. In addition we discuss the frequency dependent shear
viscosity evaluated within the same model and compare our theoretical results
with recent experiments in microgravity.Comment: 17 pages, 12 figure
Critical slowing down in random anisotropy magnets
We study the purely relaxational critical dynamics with non-conserved order
parameter (model A critical dynamics) for three-dimensional magnets with
disorder in a form of the random anisotropy axis. For the random axis
anisotropic distribution, the static asymptotic critical behaviour coincides
with that of random site Ising systems. Therefore the asymptotic critical
dynamics is governed by the dynamical exponent of the random Ising model.
However, the disorder influences considerably the dynamical behaviour in the
non-asymptotic regime. We perform a field-theoretical renormalization group
analysis within the minimal subtraction scheme in two-loop approximation to
investigate asymptotic and effective critical dynamics of random anisotropy
systems. The results demonstrate the non-monotonic behaviour of the dynamical
effective critical exponent .Comment: 11 pages, 4 figures, style file include
Entropic equation of state and scaling functions near the critical point in scale-free networks
We analyze the entropic equation of state for a many-particle interacting
system in a scale-free network. The analysis is performed in terms of scaling
functions which are of fundamental interest in the theory of critical phenomena
and have previously been theoretically and experimentally explored in the
context of various magnetic, fluid, and superconducting systems in two and
three dimensions. Here, we obtain general scaling functions for the entropy,
the constant-field heat capacity, and the isothermal magnetocaloric coefficient
near the critical point in scale-free networks, where the node-degree
distribution exponent appears to be a global variable and plays a
crucial role, similar to the dimensionality for systems on lattices. This
extends the principle of universality to systems on scale-free networks and
allows quantification of the impact of fluctuations in the network structure on
critical behavior.Comment: 8 pages, 4 figure
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