331 research outputs found
Reconstructed Rough Growing Interfaces; Ridgeline Trapping of Domain Walls
We investigate whether surface reconstruction order exists in stationary
growing states, at all length scales or only below a crossover length, . The later would be similar to surface roughness in growing crystal
surfaces; below the equilibrium roughening temperature they evolve in a
layer-by-layer mode within a crossover length scale , but are always
rough at large length scales. We investigate this issue in the context of KPZ
type dynamics and a checker board type reconstruction, using the restricted
solid-on-solid model with negative mono-atomic step energies. This is a
topology where surface reconstruction order is compatible with surface
roughness and where a so-called reconstructed rough phase exists in
equilibrium. We find that during growth, reconstruction order is absent in the
thermodynamic limit, but exists below a crossover length , and that this local order fluctuates critically. Domain walls become
trapped at the ridge lines of the rough surface, and thus the reconstruction
order fluctuations are slaved to the KPZ dynamics
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
The Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential U. The Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap. Explicit expressions have been obtained for the Hall conductance for both large and small U/ℏωc
Preroughening, Diffusion, and Growth of An FCC(111) Surface
Preroughening of close-packed fcc(111) surfaces, found in rare gas solids, is
an interesting, but poorly characterized phase transition. We introduce a
restricted solid-on-solid model, named FCSOS, which describes it. Using mostly
Monte Carlo, we study both statics, including critical behavior and scattering
properties, and dynamics, including surface diffusion and growth. In antiphase
scattering, it is shown that preroughening will generally show up at most as a
dip. Surface growth is predicted to be continuous at preroughening, where
surface self-diffusion should also drop. The physical mechanism leading to
preroughening on rare gas surfaces is analysed, and identified in the step-step
elastic repulsion.Comment: Revtex + uuencoded figures, to appear in Physical Review Letter
An exact universal amplitude ratio for percolation
The universal amplitude ratio for percolation in two
dimensions is determined exactly using results for the dilute A model in regime
1, by way of a relationship with the q-state Potts model for q<4.Comment: 5 pages, LaTeX, submitted to J. Phys. A. One paragraph rewritten to
correct error
Roughening Induced Deconstruction in (100) Facets of CsCl Type Crystals
The staggered 6-vertex model describes the competition between surface
roughening and reconstruction in (100) facets of CsCl type crystals. Its phase
diagram does not have the expected generic structure, due to the presence of a
fully-packed loop-gas line. We prove that the reconstruction and roughening
transitions cannot cross nor merge with this loop-gas line if these degrees of
freedom interact weakly. However, our numerical finite size scaling analysis
shows that the two critical lines merge along the loop-gas line, with strong
coupling scaling properties. The central charge is much larger than 1.5 and
roughening takes place at a surface roughness much larger than the conventional
universal value. It seems that additional fluctuations become critical
simultaneously.Comment: 31 pages, 9 figure
Anomalous Roughness in Dimer-Type Surface Growth
We point out how geometric features affect the scaling properties of
non-equilibrium dynamic processes, by a model for surface growth where
particles can deposit and evaporate only in dimer form, but dissociate on the
surface. Pinning valleys (hill tops) develop spontaneously and the surface
facets for all growth (evaporation) biases. More intriguingly, the scaling
properties of the rough one dimensional equilibrium surface are anomalous. Its
width, , diverges with system size , as
instead of the conventional universal value . This originates
from a topological non-local evenness constraint on the surface configurations.Comment: Published version in PR
Universal amplitude of the free energy density in finite-size scaling: the Potts universality
Using the numerical results of the finite-size scaling study of the q-state
Potts model by Bloete and Nightingale, we obtain conjectured expressions for
the universal amplitude of the free energy density.Comment: Old paper, for archiving. 4 pages, IOP macr
Dynamical correlations and quantum phase transition in the quantum Potts model
We present a detailed study of the finite temperature dynamical properties of
the quantum Potts model in one dimension.Quasiparticle excitations in this
model have internal quantum numbers, and their scattering matrix {\gf deep} in
the gapped phases is shown to take a simple {\gf exchange} form in the
perturbative regimes. The finite temperature correlation functions in the
quantum critical regime are determined using conformal invariance, while {\gf
far from the quantum critical point} we compute the decay functions
analytically within a semiclassical approach of Sachdev and Damle [K. Damle and
S. Sachdev, Phys. Rev. B \textbf{57}, 8307 (1998)]. As a consequence, decay
functions exhibit a {\em diffusive character}. {\gf We also provide robust
arguments that our semiclassical analysis carries over to very low temperatures
even in the vicinity of the quantum phase transition.} Our results are also
relevant for quantum rotor models, antiferromagnetic chains, and some spin
ladder systems.Comment: 18 PRB pages added correction
Finite-Size Scaling in Two-dimensional Continuum Percolation Models
We test the universal finite-size scaling of the cluster mass order parameter
in two-dimensional (2D) isotropic and directed continuum percolation models
below the percolation threshold by computer simulations. We found that the
simulation data in the 2D continuum models obey the same scaling expression of
mass M to sample size L as generally accepted for isotropic lattice problems,
but with a positive sign of the slope in the ln-ln plot of M versus L. Another
interesting aspect of the finite-size 2D models is also suggested by plotting
the normalized mass in 2D continuum and lattice bond percolation models, versus
an effective percolation parameter, independently of the system structure (i.e.
lattice or continuum) and of the possible directions allowed for percolation
(i.e. isotropic or directed) in regions close to the percolation thresholds.
Our study is the first attempt to map the scaling behaviour of the mass for
both lattice and continuum model systems into one curve.Comment: 9 pages, Revtex, 2 PostScript figure
- …