82 research outputs found
Exact Renormalization-Group Study of Aperiodic Ising Quantum Chains and Directed Walks
We consider the Ising model and the directed walk on two-dimensional layered
lattices and show that the two problems are inherently related: The zero-field
thermodynamical properties of the Ising model are contained in the spectrum of
the transfer matrix of the directed walk. The critical properties of the two
models are connected to the scaling behavior of the eigenvalue spectrum of the
transfer matrix which is studied exactly through renormalization for different
self-similar distributions of the couplings. The models show very rich bulk and
surface critical behaviors with nonuniversal critical exponents,
coupling-dependent anisotropic scaling, first-order surface transition, and
stretched exponential critical correlations. It is shown that all the
nonuniversal critical exponents obtained for the aperiodic Ising models satisfy
scaling relations and can be expressed as functions of varying surface magnetic
exponents.Comment: 22 pages, 8 eps-figures, uses RevTex and epsf, minor correction
Fluctuations of steps on crystal surfaces
Fluctuations of isolated and pairs of ascending steps of monoatomic height
are studied in the framework of SOS models, using mainly Monte Carlo
techniques. Below the roughening transistion of the surface, the profiles of
long steps show the same scaling features for terrace and surface diffusion.
For a pair of short steps, their separation distance is found to grow as
at late stages. Above roughening, simulational data on surface
diffusion agree well with the classical continuum theory of Mullins.Comment: 4 pages, 2 eps figure
Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions
A combination of recent numerical and theoretical advances are applied to
analyze the scaling behaviour of the site-diluted Ising model in two
dimensions, paying special attention to the implications for multiplicative
logarithmic corrections. The analysis focuses primarily on the odd sector of
the model (i.e., that associated with magnetic exponents), and in particular on
its Lee-Yang zeros, which are determined to high accuracy. Scaling relations
are used to connect to the even (thermal) sector, and a first analysis of the
density of zeros yields information on the specific heat and its corrections.
The analysis is fully supportive of the strong scaling hypothesis and of the
scaling relations for logarithmic corrections.Comment: 15 pages, 3 figures. Published versio
The Effects of Next-Nearest-Neighbor Interactions on the Orientation Dependence of Step Stiffness: Reconciling Theory with Experiment for Cu(001)
Within the solid-on-solid (SOS) approximation, we carry out a calculation of
the orientational dependence of the step stiffness on a square lattice with
nearest and next-nearest neighbor interactions. At low temperature our result
reduces to a simple, transparent expression. The effect of the strongest trio
(three-site, non pairwise) interaction can easily be incorporated by modifying
the interpretation of the two pairwise energies. The work is motivated by a
calculation based on nearest neighbors that underestimates the stiffness by a
factor of 4 in directions away from close-packed directions, and a subsequent
estimate of the stiffness in the two high-symmetry directions alone that
suggested that inclusion of next-nearest-neighbor attractions could fully
explain the discrepancy. As in these earlier papers, the discussion focuses on
Cu(001).Comment: 8 pages, 3 figures, submitted to Phys. Rev.
Surface critical behavior of two-dimensional dilute Ising models
Ising models with nearest-neighbor ferromagnetic random couplings on a square
lattice with a (1,1) surface are studied, using Monte Carlo techniques and
star-tiangle transformation method. In particular, the critical exponent of the
surface magnetization is found to be close to that of the perfect model,
beta_s=1/2. The crossover from surface to bulk critical properties is
discussed.Comment: 6 pages in RevTex, 3 ps figures, to appear in Journal of Stat. Phy
Correlations in nano-scale step fluctuations: comparison of simulation and experiments
We analyze correlations in step-edge fluctuations using the
Bortz-Kalos-Lebowitz kinetic Monte Carlo algorithm, with a 2-parameter
expression for energy barriers, and compare with our VT-STM line-scan
experiments on spiral steps on Pb(111). The scaling of the correlation times
gives a dynamic exponent confirming the expected step-edge-diffusion
rate-limiting kinetics both in the MC and in the experiments. We both calculate
and measure the temperature dependence of (mass) transport properties via the
characteristic hopping times and deduce therefrom the notoriously-elusive
effective energy barrier for the edge fluctuations. With a careful analysis we
point out the necessity of a more complex model to mimic the kinetics of a
Pb(111) surface for certain parameter ranges.Comment: 10 pages, 9 figures, submitted to Physical Review
Dynamics of surface steps
In the framework of SOS models, the dynamics of isolated and pairs of surface
steps of monoatomic height is studied, for step--edge diffusion and for
evaporation kinetics, using Monte Carlo techniques. In particular, various
interesting crossover phenomena are identified. Simulational results are
compared, especially, to those of continuum theories and random walk
descriptions.Comment: 13 pages in elsart style, 4 eps figures, submitted to Physica
Boundary critical behaviour of two-dimensional random Ising models
Using Monte Carlo techniques and a star-triangle transformation, Ising models
with random, 'strong' and 'weak', nearest-neighbour ferromagnetic couplings on
a square lattice with a (1,1) surface are studied near the phase transition.
Both surface and bulk critical properties are investigated. In particular, the
critical exponents of the surface magnetization, 'beta_1', of the correlation
length, 'nu', and of the critical surface correlations, 'eta_{\parallel}', are
analysed.Comment: 16 pages in ioplppt style, 7 ps figures, submitted to J. Phys.
Fluctuations, line tensions, and correlation times of nanoscale islands on surfaces
We analyze in detail the fluctuations and correlations of the (spatial)
Fourier modes of nano-scale single-layer islands on (111) fcc crystal surfaces.
We analytically show that the Fourier modes of the fluctuations couple due to
the anisotropy of the crystal, changing the power spectrum of the fluctuations,
and that the actual eigenmodes of the fluctuations are the appropriate linear
combinations of the Fourier modes. Using kinetic Monte Carlo simulations with
bond-counting parameters that best match realistic energy barriers for hopping
rates, we deduce absolute line tensions as a function of azimuthal orientation
from the analyses of the fluctuation of each individual mode. The
autocorrelation functions of these modes give the scaling of the correlation
times with wavelength, providing us with the rate-limiting kinetics driving the
fluctuations, here step-edge diffusion. The results for the energetic
parameters are in reasonable agreement with available experimental data for
Pb(111) surfaces, and we compare the correlation times of island-edge
fluctuations to relaxation times of quenched Pb crystallites.Comment: 11 pages, 8 figures; to appear in PRB 70, xxx (15 Dec 2004), changes
in MC and its implication
Nanoscale Equilibrium Crystal Shapes
The finite size and interface effects on equilibrium crystal shape (ECS) have
been investigated for the case of a surface free energy density including step
stiffness and inverse-square step-step interactions. Explicitly including the
curvature of a crystallite leads to an extra boundary condition in the solution
of the crystal shape, yielding a family of crystal shapes, governed by a shape
parameter c. The total crystallite free energy, including interface energy, is
minimized for c=0, yielding in all cases the traditional PT shape (z x3/2).
Solutions of the crystal shape for c≠0 are presented and discussed in the
context of meta-stable states due to the energy barrier for nucleation.
Explicit scaled relationships for the ECS and meta-stable states in terms of
the measurable step parameters and the interfacial energy are presented.Comment: 35 page
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