55 research outputs found
Application of Minimal Subtraction Renormalization to Crossover Behavior near the He Liquid-Vapor Critical Point
Parametric expressions are used to calculate the isothermal susceptibility,
specific heat, order parameter, and correlation length along the critical
isochore and coexistence curve from the asymptotic region to crossover region.
These expressions are based on the minimal-subtraction renormalization scheme
within the model. Using two adjustable parameters in these
expressions, we fit the theory globally to recently obtained experimental
measurements of isothermal susceptibility and specific heat along the critical
isochore and coexistence curve, and early measurements of coexistence curve and
light scattering intensity along the critical isochore of He near its
liquid-vapor critical point. The theory provides good agreement with these
experimental measurements within the reduced temperature range
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
Synthesis of intermetallic hydrogen storage materials based on TI-CR by glow discharge plasma
The TiCr2 intermetallic compound with the C36 hexagonal Laves phase has been synthesized by glow discharge plasma. The hydrogen absorption-desorption properties of the obtained alloy were investigated. It is shown that hydrogen storage capacity of material was 0.43 wt % at 85 °C and 8 atm
Five-loop additive renormalization in the phi^4 theory and amplitude functions of the minimally renormalized specific heat in three dimensions
We present an analytic five-loop calculation for the additive renormalization
constant A(u,epsilon) and the associated renormalization-group function B(u) of
the specific heat of the O(n) symmetric phi^4 theory within the minimal
subtraction scheme. We show that this calculation does not require new
five-loop integrations but can be performed on the basis of the previous
five-loop calculation of the four-point vertex function combined with an
appropriate identification of symmetry factors of vacuum diagrams. We also
determine the amplitude functions of the specific heat in three dimensions for
n=1,2,3 above T_c and for n=1 below T_c up to five-loop order. Accurate results
are obtained from Borel resummations of B(u) for n=1,2,3 and of the amplitude
functions for n=1. Previous conjectures regarding the smallness of the resummed
higher-order contributions are confirmed. Borel resummed universal amplitude
ratios A^+/A^- and a_c^+/a_c^- are calculated for n=1.Comment: 30 pages REVTeX, 3 PostScript figures, submitted to Phys. Rev.
Effective critical behaviour of diluted Heisenberg-like magnets
In agreement with the Harris criterion, asymptotic critical exponents of
three-dimensional (3d) Heisenberg-like magnets are not influenced by weak
quenched dilution of non-magnetic component. However, often in the experimental
studies of corresponding systems concentration- and temperature-dependent
exponents are found with values differing from those of the 3d Heisenberg
model.
In our study, we use the field--theoretical renormalization group approach to
explain this observation and to calculate the effective critical exponents of
weakly diluted quenched Heisenberg-like magnet. Being non-universal, these
exponents change with distance to the critical point as observed
experimentally. In the asymptotic limit (at ) they equal to the critical
exponents of the pure 3d Heisenberg magnet as predicted by the Harris
criterion.Comment: 15 pages, 4 figure
Crossover from Isotropic to Directed Percolation
Percolation clusters are probably the simplest example for scale--invariant
structures which either are governed by isotropic scaling--laws
(``self--similarity'') or --- as in the case of directed percolation --- may
display anisotropic scaling behavior (``self--affinity''). Taking advantage of
the fact that both isotropic and directed bond percolation (with one preferred
direction) may be mapped onto corresponding variants of (Reggeon) field theory,
we discuss the crossover between self--similar and self--affine scaling. This
has been a long--standing and yet unsolved problem because it is accompanied by
different upper critical dimensions: for isotropic, and
for directed percolation, respectively. Using a generalized
subtraction scheme we show that this crossover may nevertheless be treated
consistently within the framework of renormalization group theory. We identify
the corresponding crossover exponent, and calculate effective exponents for
different length scales and the pair correlation function to one--loop order.
Thus we are able to predict at which characteristic anisotropy scale the
crossover should occur. The results are subject to direct tests by both
computer simulations and experiment. We emphasize the broad range of
applicability of the proposed method.Comment: 19 pages, written in RevTeX, 12 figures available upon request (from
[email protected] or [email protected]), EF/UCT--94/2, to be
published in Phys. Rev. E (May 1994
Renormalization group and 1/N expansion for 3-dimensional Ginzburg-Landau-Wilson models
A renormalization-group scheme is developed for the 3-dimensional
O()-symmetric Ginzburg-Landau-Wilson model, which is consistent with the
use of a 1/N expansion as a systematic method of approximation. It is motivated
by an application to the critical properties of superconductors, reported in a
separate paper. Within this scheme, the infrared stable fixed point controlling
critical behaviour appears at , where is the inverse of
the quartic coupling constant, and an efficient renormalization procedure
consists in the minimal subtraction of ultraviolet divergences at . This
scheme is implemented at next-to-leading order, and the standard results for
critical exponents calculated by other means are recovered. An apparently novel
result of this non-perturbative method of approximation is that corrections to
scaling (or confluent singularities) do not, as in perturbative analyses,
appear as simple power series in the variable . At least in
three dimensions, the power series are modified by powers of .Comment: 20 pages; 5 figure
Critical Viscosity Exponent for Fluids: What Happend to the Higher Loops
We arrange the loopwise perturbation theory for the critical viscosity
exponent , which happens to be very small, as a power series in
itself and argue that the effect of loops beyond two is negligible.
We claim that the critical viscosity exponent should be very closely
approximated by .Comment: 9 pages and 3 figure
Model C critical dynamics of random anisotropy magnets
We study the relaxational critical dynamics of the three-dimensional random
anisotropy magnets with the non-conserved n-component order parameter coupled
to a conserved scalar density. In the random anisotropy magnets the structural
disorder is present in a form of local quenched anisotropy axes of random
orientation. When the anisotropy axes are randomly distributed along the edges
of the n-dimensional hypercube, asymptotical dynamical critical properties
coincide with those of the random-site Ising model. However structural disorder
gives rise to considerable effects for non-asymptotic critical dynamics. We
investigate this phenomenon by a field-theoretical renormalization group
analysis in the two-loop order. We study critical slowing down and obtain
quantitative estimates for the effective and asymptotic critical exponents of
the order parameter and scalar density. The results predict complex scenarios
for the effective critical exponent approaching an asymptotic regime.Comment: 8 figures, style files include
The finite-temperature chiral transition in QCD with adjoint fermions
We study the nature of the finite-temperature chiral transition in QCD with
N_f light quarks in the adjoint representation (aQCD). Renormalization-group
arguments show that the transition can be continuous if a stable fixed point
exists in the renormalization-group flow of the corresponding three-dimensional
Phi^4 theory with a complex 2N_f x 2N_f symmetric matrix field and
symmetry-breaking pattern SU(2N_f)->SO(2N_f). This issue is investigated by
exploiting two three-dimensional perturbative approaches, the massless
minimal-subtraction scheme without epsilon expansion and a massive scheme in
which correlation functions are renormalized at zero momentum. We compute the
renormalization-group functions in the two schemes to five and six loops
respectively, and determine their large-order behavior.
The analyses of the series show the presence of a stable three-dimensional
fixed point characterized by the symmetry-breaking pattern SU(4)->SO(4). This
fixed point does not appear in an epsilon-expansion analysis and therefore does
not exist close to four dimensions. The finite-temperature chiral transition in
two-flavor aQCD can therefore be continuous; in this case its critical behavior
is determined by this new SU(4)/SO(4) universality class. One-flavor aQCD may
show a more complex phase diagram with two phase transitions. One of them, if
continuous, should belong to the O(3) vector universality class.Comment: 36 page
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