32 research outputs found
Preroughening transitions in a model for Si and Ge (001) type crystal surfaces
The uniaxial structure of Si and Ge (001) facets leads to nontrivial
topological properties of steps and hence to interesting equilibrium phase
transitions. The disordered flat phase and the preroughening transition can be
stabilized without the need for step-step interactions. A model describing this
is studied numerically by transfer matrix type finite-size-scaling of interface
free energies. Its phase diagram contains a flat, rough, and disordered flat
phase, separated by roughening and preroughening transition lines. Our estimate
for the location of the multicritical point where the preroughening line merges
with the roughening line, predicts that Si and Ge (001) undergo preroughening
induced simultaneous deconstruction transitions.Comment: 13 pages, RevTex, 7 Postscript Figures, submitted to J. Phys.
Dynamic instability transitions in 1D driven diffusive flow with nonlocal hopping
One-dimensional directed driven stochastic flow with competing nonlocal and
local hopping events has an instability threshold from a populated phase into
an empty-road (ER) phase. We implement this in the context of the asymmetric
exclusion process. The nonlocal skids promote strong clustering in the
stationary populated phase. Such clusters drive the dynamic phase transition
and determine its scaling properties. We numerically establish that the
instability transition into the ER phase is second order in the regime where
the entry point reservoir controls the current and first order in the regime
where the bulk is in control. The first order transition originates from a
turn-about of the cluster drift velocity. At the critical line, the current
remains analytic, the road density vanishes linearly, and fluctuations scale as
uncorrelated noise. A self-consistent cluster dynamics analysis explains why
these scaling properties remain that simple.Comment: 11 pages, 14 figures (25 eps files); revised as the publised versio
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
Crossover Scaling Functions in One Dimensional Dynamic Growth Models
The crossover from Edwards-Wilkinson () to KPZ () type growth is
studied for the BCSOS model. We calculate the exact numerical values for the
and massgap for using the master equation. We predict
the structure of the crossover scaling function and confirm numerically that
and , with . KPZ type growth is
equivalent to a phase transition in meso-scopic metallic rings where attractive
interactions destroy the persistent current; and to endpoints of facet-ridges
in equilibrium crystal shapes.Comment: 11 pages, TeX, figures upon reques