832 research outputs found
Short-time critical dynamics of the three-dimensional systems with long-range correlated disorder
Monte Carlo simulations of the short-time dynamic behavior are reported for
three-dimensional Ising and XY models with long-range correlated disorder at
criticality, in the case corresponding to linear defects. The static and
dynamic critical exponents are determined for systems starting separately from
ordered and disordered initial states. The obtained values of the exponents are
in a good agreement with results of the field-theoretic description of the
critical behavior of these models in the two-loop approximation and with our
results of Monte Carlo simulations of three-dimensional Ising model in
equilibrium state.Comment: 24 RevTeX pages, 12 figure
The influence of long-range correlated defects on critical ultrasound propagation in solids
The effect of long-range correlated quenched structural defects on the
critical ultrasound attenuation and sound velocity dispersion is studied for
three-dimensional Ising-like systems. A field-theoretical description of the
dynamic critical effects of ultrasound propagation in solids is performed with
allowance for both fluctuation and relaxation attenuation mechanisms. The
temperature and frequency dependences of the dynamical scaling functions of the
ultrasound critical characteristics are calculated in a two-loop approximation
for different values of the correlation parameter of the Weinrib-Halperin
model with long-range correlated defects. The asymptotic behavior of the
dynamical scaling functions in hydrodynamic and critical regions is separated.
The influence of long-range correlated disorder on the asymptotic behavior of
the critical ultrasonic anomalies is discussed.Comment: 12 RevTeX pages, 3 figure
Relaxational dynamics in 3D randomly diluted Ising models
We study the purely relaxational dynamics (model A) at criticality in
three-dimensional disordered Ising systems whose static critical behaviour
belongs to the randomly diluted Ising universality class. We consider the
site-diluted and bond-diluted Ising models, and the +- J Ising model along the
paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations
at the critical point using the Metropolis algorithm and study the dynamic
behaviour in equilibrium at various values of the disorder parameter. The
results provide a robust evidence of the existence of a unique model-A dynamic
universality class which describes the relaxational critical dynamics in all
considered models. In particular, the analysis of the size-dependence of
suitably defined autocorrelation times at the critical point provides the
estimate z=2.35(2) for the universal dynamic critical exponent. We also study
the off-equilibrium relaxational dynamics following a quench from T=\infty to
T=T_c. In agreement with the field-theory scenario, the analysis of the
off-equilibrium dynamic critical behavior gives an estimate of z that is
perfectly consistent with the equilibrium estimate z=2.35(2).Comment: 38 page
Critical behavior of disordered systems with replica symmetry breaking
A field-theoretic description of the critical behavior of weakly disordered
systems with a -component order parameter is given. For systems of an
arbitrary dimension in the range from three to four, a renormalization group
analysis of the effective replica Hamiltonian of the model with an interaction
potential without replica symmetry is given in the two-loop approximation. For
the case of the one-step replica symmetry breaking, fixed points of the
renormalization group equations are found using the Pade-Borel summing
technique. For every value , the threshold dimensions of the system that
separate the regions of different types of the critical behavior are found by
analyzing those fixed points. Specific features of the critical behavior
determined by the replica symmetry breaking are described. The results are
compared with those obtained by the -expansion and the scope of the
method applicability is determined.Comment: 18 pages, 2 figure
Effect of structural defects on anomalous ultrasound propagation in solids during second-order phase transitions
The effect of structural defects on the critical ultrasound attenuation and
ultrasound velocity dispersion in Ising-like three-dimensional systems is
studied. A field-theoretical description of the dynamic effects of
acoustic-wave propagation in solids during phase transitions is performed with
allowance for both fluctuation and relaxation attenuation mechanisms. The
temperature and frequency dependences of the scaling functions of the
attenuation coefficient and the ultrasound velocity dispersion are calculated
in a two-loop approximation for pure and structurally disordered systems, and
their asymptotic behavior in hydrodynamic and critical regions is separated. As
compared to a pure system, the presence of structural defects in it is shown to
cause a stronger increase in the sound attenuation coefficient and the sound
velocity dispersion even in the hydrodynamic region as the critical temperature
is reached. As compared to pure analogs, structurally disordered systems should
exhibit stronger temperature and frequency dependences of the acoustic
characteristics in the critical region.Comment: 7 RevTeX pages, 4 figure
Critical Behaviour of 3D Systems with Long-Range Correlated Quenched Defects
A field-theoretic description of the critical behaviour of systems with
quenched defects obeying a power law correlations for
large separations is given. Directly for three-dimensional systems
and different values of correlation parameter a
renormalization analysis of scaling function in the two-loop approximation is
carried out, and the fixed points corresponding to stability of the various
types of critical behaviour are identified. The obtained results essentially
differ from results evaluated by double - expansion. The
critical exponents in the two-loop approximation are calculated with the use of
the Pade-Borel summation technique.Comment: Submitted to J. Phys. A, Letter to Editor 9 pages, 4 figure
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