55 research outputs found
Critical properties of loop percolation models with optimization constraints
We study loop percolation models in two and in three space dimensions, in
which configurations of occupied bonds are forced to form closed loop. We show
that the uncorrelated occupation of elementary plaquettes of the square and the
simple cubic lattice by elementary loops leads to a percolation transition that
is in the same universality class as the conventional bond percolation. In
contrast to this an optimization constraint for the loop configurations, which
then have to minimize a particular generic energy function, leads to a
percolation transition that constitutes a new universality class, for which we
report the critical exponents. Implication for the physics of solid-on-solid
and vortex glass models are discussed.Comment: 8 pages, 8 figure
Spin magnetization of strongly correlated electron gas confined in a two-dimensional finite lattice
The influence of disorder and interaction on the ground state polarization of
the two-dimensional (2D) correlated electron gas is studied by numerical
investigations of unrestricted Hartree-Fock equations. The ferromagnetic ground
state is found to be plausible when the electron number is lowered and the
interaction and disorder parameters are suitably chosen. For a finite system at
constant electronic density the disorder induced spin polarization is cut off
when the electron orbitals become strongly localized to the individual network
sites. The fluctuations of the interaction matrix elements are calculated and
brought out as favoring the ferromagnetic instability in the extended and weak
localization regime. The localization effect of the Hubbard interaction term is
discussed.Comment: 7 pages, 9 figure
Dynamic renormalization group study of a generalized continuum model of crystalline surfaces
We apply the Nozieres-Gallet dynamic renormalization group (RG) scheme to a
continuum equilibrium model of a d-dimensional surface relaxing by linear
surface tension and linear surface diffusion, and which is subject to a lattice
potential favoring discrete values of the height variable. The model thus
interpolates between the overdamped sine-Gordon model and a related continuum
model of crystalline tensionless surfaces. The RG flow predicts the existence
of an equilibrium roughening transition only for d = 2 dimensional surfaces,
between a flat low-temperature phase and a rough high-temperature phase in the
Edwards-Wilkinson (EW) universality class. The surface is always in the flat
phase for any other substrate dimensions d > 2. For any value of d, the linear
surface diffusion mechanism is an irrelevant perturbation of the linear surface
tension mechanism, but may induce long crossovers within which the scaling
properties of the linear molecular-beam epitaxy equation are observed, thus
increasing the value of the sine-Gordon roughening temperature. This phenomenon
originates in the non-linear lattice potential, and is seen to occur even in
the absence of a bare surface tension term. An important consequence of this is
that a crystalline tensionless surface is asymptotically described at high
temperatures by the EW universality class.Comment: 22 pages, 5 figures. Accepted for publication in Physical Review
Two-Dimensional Wigner Crystal in Anisotropic Semiconductor
We investigate the effect of mass anisotropy on the Wigner crystallization
transition in a two-dimensional (2D) electron gas. The static and dynamical
properties of a 2D Wigner crystal have been calculated for arbitrary 2D Bravais
lattices in the presence of anisotropic mass, as may be obtainable in Si
MOSFETs with (110) surface. By studying the stability of all possible lattices,
we find significant change in the crystal structure and melting density of the
electron lattice with the lowest ground state energy.Comment: 4 pages, revtex, 4 figure
On The Mobile Behavior of Solid He at High Temperatures
We report studies of solid helium contained inside a torsional oscillator, at
temperatures between 1.07K and 1.87K. We grew single crystals inside the
oscillator using commercially pure He and He-He mixtures containing
100 ppm He. Crystals were grown at constant temperature and pressure on the
melting curve. At the end of the growth, the crystals were disordered,
following which they partially decoupled from the oscillator. The fraction of
the decoupled He mass was temperature and velocity dependent. Around 1K, the
decoupled mass fraction for crystals grown from the mixture reached a limiting
value of around 35%. In the case of crystals grown using commercially pure
He at temperatures below 1.3K, this fraction was much smaller. This
difference could possibly be associated with the roughening transition at the
solid-liquid interface.Comment: 15 pages, 6 figure
Universality in the Screening Cloud of Dislocations Surrounding a Disclination
A detailed analytical and numerical analysis for the dislocation cloud
surrounding a disclination is presented. The analytical results show that the
combined system behaves as a single disclination with an effective fractional
charge which can be computed from the properties of the grain boundaries
forming the dislocation cloud. Expressions are also given when the crystal is
subjected to an external two-dimensional pressure. The analytical results are
generalized to a scaling form for the energy which up to core energies is given
by the Young modulus of the crystal times a universal function. The accuracy of
the universality hypothesis is numerically checked to high accuracy. The
numerical approach, based on a generalization from previous work by S. Seung
and D.R. Nelson ({\em Phys. Rev A 38:1005 (1988)}), is interesting on its own
and allows to compute the energy for an {\em arbitrary} distribution of
defects, on an {\em arbitrary geometry} with an arbitrary elastic {\em energy}
with very minor additional computational effort. Some implications for recent
experimental, computational and theoretical work are also discussed.Comment: 35 pages, 21 eps file
Dynamically turning off interactions in a two component condensate
We propose a mechanism to change the interaction strengths of a two component
condensate. It is shown that the application of pi/2 pulses allows to alter the
effective interspecies interaction strength as well as the effective
interaction strength between particles of the same kind. This mechanism
provides a simple method to transform spatially stable condensates into
unstable once and vice versa. It also provides a means to store a squeezed spin
state by turning off the interaction for the internal states and thus allows to
gain control over many body entangled states.Comment: 7 pages 5 figures, symbols changed, minor changes, to appear in Phys.
Rev.
Velocity-force characteristics of an interface driven through a periodic potential
We study the creep dynamics of a two-dimensional interface driven through a
periodic potential using dynamical renormalization group methods. We find that
the nature of weak-drive transport depends qualitatively on whether the
temperature is above or below the equilibrium roughening transition
temperature . Above , the velocity-force characteristics is Ohmic,
with linear mobility exhibiting a jump discontinuity across the transition. For
, the transport is highly nonlinear, exhibiting an interesting
crossover in temperature and weak external force . For intermediate drive,
, we find near a power-law velocity-force characteristics
, with , and well-below ,
, with . In the limit
of vanishing drive () the velocity-force characteristics crosses over
to , and is controlled by soliton nucleation.Comment: 18 pages, submitted to Phys. Rev.
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