1,693 research outputs found
Length and time scale divergences at the magnetization-reversal transition in the Ising model
The divergences of both the length and time scales, at the magnetization-
reversal transition in Ising model under a pulsed field, have been studied in
the linearized limit of the mean field theory. Both length and time scales are
shown to diverge at the transition point and it has been checked that the
nature of the time scale divergence agrees well with the result obtained from
the numerical solution of the mean field equation of motion. Similar growths in
length and time scales are also observed, as one approaches the transition
point, using Monte Carlo simulations. However, these are not of the same nature
as the mean field case. Nucleation theory provides a qualitative argument which
explains the nature of the time scale growth. To study the nature of growth of
the characteristic length scale, we have looked at the cluster size
distribution of the reversed spin domains and defined a pseudo-correlation
length which has been observed to grow at the phase boundary of the transition.Comment: 9 pages Latex, 3 postscript figure
Quantum Annealing in a Kinetically Constrained System
Classical and quantum annealing is discussed for a kinetically constrained
chain of non-interacting asymmetric double wells, represented by Ising
spins in a longitudinal field . It is shown that in certain cases, where the
kinetic constraints may arise from infinitely high but vanishingly narrow
barriers appearing in the relaxation path of the system, quantum annealing
exploiting the quantum-mechanical penetration of sufficiently narrow barriers
may be far more efficient than its thermal counterpart.
We have used a semiclassical picture of scattering dynamics to do our
simulation for the quantum system.Comment: 5 pages, 3 figure
Mean field and Monte Carlo studies of the magnetization-reversal transition in the Ising model
Detailed mean field and Monte Carlo studies of the dynamic
magnetization-reversal transition in the Ising model in its ordered phase under
a competing external magnetic field of finite duration have been presented
here. Approximate analytical treatment of the mean field equations of motion
shows the existence of diverging length and time scales across this dynamic
transition phase boundary. These are also supported by numerical solutions of
the complete mean field equations of motion and the Monte Carlo study of the
system evolving under Glauber dynamics in both two and three dimensions.
Classical nucleation theory predicts different mechanisms of domain growth in
two regimes marked by the strength of the external field, and the nature of the
Monte Carlo phase boundary can be comprehended satisfactorily using the theory.
The order of the transition changes from a continuous to a discontinuous one as
one crosses over from coalescence regime (stronger field) to nucleation regime
(weaker field). Finite size scaling theory can be applied in the coalescence
regime, where the best fit estimates of the critical exponents are obtained for
two and three dimensions.Comment: 16 pages latex, 13 ps figures, typos corrected, references adde
Randomly Diluted e_g Orbital-Ordered Systems
Dilution effects on the long-range ordered state of the doubly degenerate
orbital are investigated. Quenched impurities without the orbital degree
of freedom are introduced in the orbital model where the long-range order is
realized by the order-from-disorder mechanism. It is shown by the Monte-Carlo
simulation and the cluster-expansion method that a decrease in the orbital
ordering temperature by dilution is remarkable in comparison with that in the
randomly diluted spin models. Tiltings of orbitals around impurity cause this
unique dilution effects on the orbital systems. The present theory provides a
new view point for the recent experiments in KCuZnF.Comment: 4 pages, 4 figure
Stick-slip statistics for two fractal surfaces: A model for earthquakes
Following the observations of the self-similarity in various length scales in
the roughness of the fractured solid surfaces, we propose here a new model for
the earthquake. We demonstrate rigorously that the contact area distribution
between two fractal surfaces follows an unique power law. This is then utilised
to show that the elastic energy releases for slips between two rough fractal
surfaces indeed follow a Guttenberg-Richter like power law.Comment: 9 pages (Latex), 4 figures (postscript
Duality and phase diagram of one dimensional transport
The observation of duality by Mukherji and Mishra in one dimensional
transport problems has been used to develop a general approach to classify and
characterize the steady state phase diagrams. The phase diagrams are determined
by the zeros of a set of coarse-grained functions without the need of detailed
knowledge of microscopic dynamics. In the process, a new class of
nonequilibrium multicritical points has been identified.Comment: 6 pages, 2 figures (4 eps files
A Green's function decoupling scheme for the Edwards fermion-boson model
Holes in a Mott insulator are represented by spinless fermions in the
fermion-boson model introduced by Edwards. Although the physically interesting
regime is for low to moderate fermion density the model has interesting
properties over the whole density range. It has previously been studied at
half-filling in the one-dimensional (1D) case by numerical methods, in
particular exact diagonalization and density matrix renormalization group
(DMRG). In the present study the one-particle Green's function is calculated
analytically by means of a decoupling scheme for the equations of motion, valid
for arbitrary density in 1D, 2D and 3D with fairly large boson energy and zero
boson relaxation parameter. The Green's function is used to compute some ground
state properties, and the one-fermion spectral function, for fermion densities
n=0.1, 0.5 and 0.9 in the 1D case. The results are generally in good agreement
with numerical results obtained by DMRG and dynamical DMRG and new light is
shed on the nature of the ground state at different fillings. The Green's
function approximation is sufficiently successful in 1D to justify future
application to the 2D and 3D cases.Comment: 19 pages, 7 figures, final version with updated reference
Classical evolution of fractal measures on the lattice
We consider the classical evolution of a lattice of non-linear coupled
oscillators for a special case of initial conditions resembling the equilibrium
state of a macroscopic thermal system at the critical point. The displacements
of the oscillators define initially a fractal measure on the lattice associated
with the scaling properties of the order parameter fluctuations in the
corresponding critical system. Assuming a sudden symmetry breaking (quench),
leading to a change in the equilibrium position of each oscillator, we
investigate in some detail the deformation of the initial fractal geometry as
time evolves. In particular we show that traces of the critical fractal measure
can sustain for large times and we extract the properties of the chain which
determine the associated time-scales. Our analysis applies generally to
critical systems for which, after a slow developing phase where equilibrium
conditions are justified, a rapid evolution, induced by a sudden symmetry
breaking, emerges in time scales much shorter than the corresponding relaxation
or observation time. In particular, it can be used in the fireball evolution in
a heavy-ion collision experiment, where the QCD critical point emerges, or in
the study of evolving fractals of astrophysical and cosmological scales, and
may lead to determination of the initial critical properties of the Universe
through observations in the symmetry broken phase.Comment: 15 pages, 15 figures, version publiced at Physical Review
1/z-renormalization of the mean-field behavior of the dipole-coupled singlet-singlet system HoF_3
The two main characteristics of the holmium ions in HoF_3 are that their
local electronic properties are dominated by two singlet states lying well
below the remaining 4f-levels, and that the classical dipole-coupling is an
order of magnitude larger than any other two-ion interactions between the
Ho-moments. This combination makes the system particularly suitable for testing
refinements of the mean-field theory. There are four Ho-ions per unit cell and
the hyperfine coupled electronic and nuclear moments on the Ho-ions order in a
ferrimagnetic structure at T_C=0.53 K. The corrections to the mean-field
behavior of holmium triflouride, both in the paramagnetic and ferrimagnetic
phase, have been calculated to first order in the high-density 1/z-expansion.
The effective medium theory, which includes the effects of the single-site
fluctuations, leads to a substantially improved description of the magnetic
properties of HoF_3, in comparison with that based on the mean-field
approximation.Comment: 26pp, plain-TeX, JJ
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