1,174 research outputs found
Off-equilibrium scaling behaviors driven by time-dependent external fields in three-dimensional O(N) vector models
We consider the dynamical off-equilibrium behavior of the three-dimensional
O vector model in the presence of a slowly-varying time-dependent
spatially-uniform magnetic field , where
is a -dimensional constant unit vector, , and is a time
scale, at fixed temperature , where corresponds to the
continuous order-disorder transition. The dynamic evolutions start from
equilibrium configurations at , correspondingly , and end at
time with , or vice versa. We show that the magnetization
displays an off-equilibrium scaling behavior close to the transition line . It arises from the interplay among the time , the time scale
, and the finite size . The scaling behavior can be parametrized in
terms of the scaling variables and , where
and are appropriate universal exponents, which differ
at the critical point and for . In the latter case, and
also depend on the shape of the lattice and on the boundary
conditions. We present numerical results for the Heisenberg () model under
a purely relaxational dynamics. They confirm the predicted off-equilibrium
scaling behaviors at and below . We also discuss hysteresis phenomena in
round-trip protocols for the time dependence of the external field. We define a
scaling function for the hysteresis loop area of the magnetization that can be
used to quantify how far the system is from equilibrium.Comment: 16 pages, extended text and ref
Critical Hysteresis from Random Anisotropy
Critical hysteresis in ferromagnets is investigated through a -component
spin model with random anisotropies, more prevalent experimentally than the
random fields used in most theoretical studies. Metastability, and the
tensorial nature of anisotropy, dictate its physics. Generically, random field
Ising criticality occurs, but other universality classes exist. In particular,
proximity to criticality may explain the discrepancy between
experiment and earlier theories. The uniaxial anisotropy constant, which can be
controlled in magnetostrictive materials by an applied stress, emerges as a
natural tuning parameter.Comment: four pages, revtex4; minor corrections in the text and typos
corrected (published version
Mean field theory for driven domain walls in disordered environments
We study the mean field equation of motion for driven domain walls in random
media. We discuss the two cases of an external constant as well as an
oscillating driving force. Our main focus lies on the critical dynamics close
to the depinning transition, which we study by analytical and numerical
methods. We find power-law scaling for the velocity as well as the hysteresis
loop area.Comment: 16 pages, 19 figures, submitted to Phys. Rev.
Scaling of hysteresis loops at phase transitions into a quasiabsorbing state
Models undergoing a phase transition to an absorbing state weakly broken by
the addition of a very low spontaneous nucleation rate are shown to exhibit
hysteresis loops whose width depends algebraically on the ramp
rate . Analytical arguments and numerical simulations show that
with , where is
the critical exponent governing the survival probability of a seed near
threshold. These results explain similar hysteresis scaling observed before in
liquid crystal convection experiments. This phenomenon is conjectured to occur
in a variety of other experimental systems.Comment: 4 pages, 4 figures, 1 tabl
Strain intermittency in shape-memory alloys
We study experimentally the intermittent progress of the mechanically induced
martensitic transformation in a Cu-Al-Be single crystal through a full-field
measurement technique: the grid method. We utilize an in- house, specially
designed gravity-based device, wherein a system controlled by water pumps
applies a perfectly monotonic uniaxial load through very small force
increments. The sample exhibits hysteretic superelastic behavior during the
forward and reverse cubic-monoclinic transformation, produced by the evolution
of the strain field of the phase microstructures. The in-plane linear strain
components are measured on the sample surface during the loading cycle, and we
characterize the strain intermittency in a number of ways, showing the
emergence of power-law behavior for the strain avalanching over almost six
decades of magnitude. We also describe the nonstationarity and the asymmetry
observed in the forward versus reverse transformation. The present experimental
approach, which allows for the monitoring of the reversible martensitic
transformation both locally and globally in the crystal, proves useful and
enhances our capabilities in the analysis and possible control of
transition-related phenomena in shape-memory alloys.Comment: Four supplementary video
Onset of Propagation of Planar Cracks in Heterogeneous Media
The dynamics of planar crack fronts in hetergeneous media near the critical
load for onset of crack motion are investigated both analytically and by
numerical simulations. Elasticity of the solid leads to long range stress
transfer along the crack front which is non-monotonic in time due to the
elastic waves in the medium. In the quasistatic limit with instantaneous stress
transfer, the crack front exhibits dynamic critical phenomenon, with a second
order like transition from a pinned to a moving phase as the applied load is
increased through a critical value. At criticality, the crack-front is
self-affine, with a roughness exponent . The dynamic
exponent is found to be equal to and the correlation length
exponent . These results are in good agreement with those
obtained from an epsilon expansion. Sound-travel time delays in the stress
transfer do not change the static exponents but the dynamic exponent
becomes exactly one. Real elastic waves, however, lead to overshoots in the
stresses above their eventual static value when one part of the crack front
moves forward. Simplified models of these stress overshoots are used to show
that overshoots are relevant at the depinning transition leading to a decrease
in the critical load and an apparent jump in the velocity of the crack front
directly to a non-zero value. In finite systems, the velocity also shows
hysteretic behaviour as a function of the loading. These results suggest a
first order like transition. Possible implications for real tensile cracks are
discussed.Comment: 51 pages + 20 figur
Anisotropic Scaling in Threshold Critical Dynamics of Driven Directed Lines
The dynamical critical behavior of a single directed line driven in a random
medium near the depinning threshold is studied both analytically (by
renormalization group) and numerically, in the context of a Flux Line in a
Type-II superconductor with a bulk current . In the absence of
transverse fluctuations, the system reduces to recently studied models of
interface depinning. In most cases, the presence of transverse fluctuations are
found not to influence the critical exponents that describe longitudinal
correlations. For a manifold with internal dimensions,
longitudinal fluctuations in an isotropic medium are described by a roughness
exponent to all orders in , and a
dynamical exponent . Transverse
fluctuations have a distinct and smaller roughness exponent
for an isotropic medium. Furthermore, their
relaxation is much slower, characterized by a dynamical exponent
, where is the
correlation length exponent. The predicted exponents agree well with numerical
results for a flux line in three dimensions. As in the case of interface
depinning models, anisotropy leads to additional universality classes. A
nonzero Hall angle, which has no analogue in the interface models, also affects
the critical behavior.Comment: 26 pages, 8 Postscript figures packed together with RevTeX 3.0
manuscript using uufiles, uses multicol.sty and epsf.sty, e-mail
[email protected] in case of problem
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