115 research outputs found
Phase Ordering of 2D XY Systems Below T_{KT}
We consider quenches in non-conserved two-dimensional XY systems between any
two temperatures below the Kosterlitz-Thouless transition. The evolving systems
are defect free at coarse-grained scales, and can be exactly treated.
Correlations scale with a characteristic length at late
times. The autocorrelation decay exponent, ,
depends on both the initial and the final state of the quench through the
respective decay exponents of equilibrium correlations, . We also discuss time-dependent quenches.Comment: LATeX 11 pages (REVTeX macros), no figure
Theory of Phase Ordering Kinetics
The theory of phase ordering dynamics -- the growth of order through domain
coarsening when a system is quenched from the homogeneous phase into a
broken-symmetry phase -- is reviewed, with the emphasis on recent developments.
Interest will focus on the scaling regime that develops at long times after the
quench. How can one determine the growth laws that describe the time-dependence
of characteristic length scales, and what can be said about the form of the
associated scaling functions? Particular attention will be paid to systems
described by more complicated order parameters than the simple scalars usually
considered, e.g. vector and tensor fields. The latter are needed, for example,
to describe phase ordering in nematic liquid crystals, on which there have been
a number of recent experiments. The study of topological defects (domain walls,
vortices, strings, monopoles) provides a unifying framework for discussing
coarsening in these different systems.Comment: To appear in Advances in Physics. 85 pages, latex, no figures. For a
hard copy with figures, email [email protected]
Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions
We have studied a quantum Hamiltonian that models an array of ultrasmall
Josephson junctions with short range Josephson couplings, , and charging
energies, , due to the small capacitance of the junctions. We derive a new
effective quantum spherical model for the array Hamiltonian. As an application
we start by approximating the capacitance matrix by its self-capacitive limit
and in the presence of an external uniform background of charges, . In
this limit we obtain the zero-temperature superconductor-insulator phase
diagram, , that improves upon previous theoretical
results that used a mean field theory approximation. Next we obtain a
closed-form expression for the conductivity of a square array, and derive a
universal scaling relation valid about the zero--temperature quantum critical
point. In the latter regime the energy scale is determined by temperature and
we establish universal scaling forms for the frequency dependence of the
conductivity.Comment: 18 pages, four Postscript figures, REVTEX style, Physical Review B
1999. We have added one important reference to this version of the pape
Surface states and Rashba-type spin polarization in antiferromagnetic MnBiTe
The layered van der Waals antiferromagnet MnBiTe has been predicted
to combine the band ordering of archetypical topological insulators such as
BiTe with the magnetism of Mn, making this material a viable candidate
for the realization of various magnetic topological states. We have
systematically investigated the surface electronic structure of
MnBiTe(0001) single crystals by use of spin- and angle-resolved
photoelectron spectroscopy experiments. In line with theoretical predictions,
the results reveal a surface state in the bulk band gap and they provide
evidence for the influence of exchange interaction and spin-orbit coupling on
the surface electronic structure.Comment: Revised versio
Response of non-equilibrium systems with long-range initial correlations
The long-time dynamics of the -dimensional spherical model with a
non-conserved order parameter and quenched from an initial state with
long-range correlations is studied through the exact calculation of the
two-time autocorrelation and autoresponse functions. In the aging regime, these
are given in terms of non-trivial universal scaling functions of both time
variables. At criticality, five distinct types of aging are found, depending on
the form of the initial correlations, while at low temperatures only a single
type of aging exists. The autocorrelation and autoreponse exponents are shown
to be generically different and to depend on the initial conditions. The
scaling form of the two-time response functions agrees with a recent prediction
coming from local scale invariance.Comment: Latex, 18pp, 2 figures (final version
Mean Field Theory of Josephson Junction Arrays with Charge Frustration
Using the path integral approach, we provide an explicit derivation of the
equation for the phase boundary for quantum Josephson junction arrays with
offset charges and non-diagonal capacitance matrix. For the model with nearest
neighbor capacitance matrix and uniform offset charge , we determine,
in the low critical temperature expansion, the most relevant contributions to
the equation for the phase boundary. We explicitly construct the charge
distributions on the lattice corresponding to the lowest energies. We find a
reentrant behavior even with a short ranged interaction. A merit of the path
integral approach is that it allows to provide an elegant derivation of the
Ginzburg-Landau free energy for a general model with charge frustration and
non-diagonal capacitance matrix. The partition function factorizes as a product
of a topological term, depending only on a set of integers, and a
non-topological one, which is explicitly evaluated.Comment: LaTex, 24 pages, 8 figure
Phase Ordering Kinetics with External Fields and Biased Initial Conditions
The late-time phase-ordering kinetics of the O(n) model for a non-conserved
order parameter are considered for the case where the O(n) symmetry is broken
by the initial conditions or by an external field. An approximate theoretical
approach, based on a `gaussian closure' scheme, is developed, and results are
obtained for the time-dependence of the mean order parameter, the pair
correlation function, the autocorrelation function, and the density of
topological defects [e.g. domain walls (), or vortices ()]. The
results are in qualitative agreement with experiments on nematic films and
related numerical simulations on the two-dimensional XY model with biased
initial conditions.Comment: 35 pages, latex, no figure
The Energy-Scaling Approach to Phase-Ordering Growth Laws
We present a simple, unified approach to determining the growth law for the
characteristic length scale, , in the phase ordering kinetics of a system
quenched from a disordered phase to within an ordered phase. This approach,
based on a scaling assumption for pair correlations, determines
self-consistently for purely dissipative dynamics by computing the
time-dependence of the energy in two ways. We derive growth laws for conserved
and non-conserved models, including two-dimensional XY models and
systems with textures. We demonstrate that the growth laws for other systems,
such as liquid-crystals and Potts models, are determined by the type of
topological defect in the order parameter field that dominates the energy. We
also obtain generalized Porod laws for systems with topological textures.Comment: LATeX 18 pages (REVTeX macros), one postscript figure appended,
REVISED --- rearranged and clarified, new paragraph on naive dimensional
analysis at end of section I
The kinetic spherical model in a magnetic field
The long-time kinetics of the spherical model in an external magnetic field
and below the equilibrium critical temperature is studied. The solution of the
associated stochastic Langevin equation is reduced exactly to a single
non-linear Volterra equation. For a sufficiently small external field, the
kinetics of the magnetization-reversal transition from the metastable to the
ground state is compared to the ageing behaviour of coarsening systems quenched
into the low-temperature phase. For an oscillating magnetic field and below the
critical temperature, we find evidence for the absence of the
frequency-dependent dynamic phase transition, which was observed previously to
occur in Ising-like systems.Comment: 26 pages, 12 figure
Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?
We study spatio-temporal fluctuations in the non-equilibrium dynamics of the
d dimensional O(N) in the large N limit. We analyse the invariance of the
dynamic equations for the global correlation and response in the slow ageing
regime under transformations of time. We find that these equations are
invariant under scale transformations. We extend this study to the action in
the dynamic generating functional finding similar results. This model therefore
falls into a different category from glassy problems in which full
time-reparametrisation invariance, a larger symmetry that emcompasses time
scale invariance, is expected to be realised asymptotically. Consequently, the
spatio-temporal fluctuations of the large N O(N) model should follow a
different pattern from that of glassy systems. We compute the fluctuations of
local, as well as spatially separated, two-field composite operators and
responses, and we confront our results with the ones found numerically for the
3d Edwards-Anderson model and kinetically constrained lattice gases. We analyse
the dependence of the fluctuations of the composite operators on the growing
domain length and we compare to what has been found in super-cooled liquids and
glasses. Finally, we show that the development of time-reparametrisation
invariance in glassy systems is intimately related to a well-defined and finite
effective temperature, specified from the modification of the
fluctuation-dissipation theorem out of equilibrium. We then conjecture that the
global asymptotic time-reparametrisation invariance is broken down to time
scale invariance in all coarsening systems.Comment: 57 pages, 5 figure
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