54,185 research outputs found
Honeycomb lattice polygons and walks as a test of series analysis techniques
We have calculated long series expansions for self-avoiding walks and
polygons on the honeycomb lattice, including series for metric properties such
as mean-squared radius of gyration as well as series for moments of the
area-distribution for polygons. Analysis of the series yields accurate
estimates for the connective constant, critical exponents and amplitudes of
honeycomb self-avoiding walks and polygons. The results from the numerical
analysis agree to a high degree of accuracy with theoretical predictions for
these quantities.Comment: 16 pages, 9 figures, jpconf style files. Presented at the conference
"Counting Complexity: An international workshop on statistical mechanics and
combinatorics." In celebration of Prof. Tony Guttmann's 60th birthda
Self-avoiding walks and polygons on the triangular lattice
We use new algorithms, based on the finite lattice method of series
expansion, to extend the enumeration of self-avoiding walks and polygons on the
triangular lattice to length 40 and 60, respectively. For self-avoiding walks
to length 40 we also calculate series for the metric properties of mean-square
end-to-end distance, mean-square radius of gyration and the mean-square
distance of a monomer from the end points. For self-avoiding polygons to length
58 we calculate series for the mean-square radius of gyration and the first 10
moments of the area. Analysis of the series yields accurate estimates for the
connective constant of triangular self-avoiding walks, ,
and confirms to a high degree of accuracy several theoretical predictions for
universal critical exponents and amplitude combinations.Comment: 24 pages, 6 figure
Elementary transitions and magnetic correlations in two-dimensional disordered nanoparticle ensembles
The magnetic relaxation processes in disordered two-dimensional ensembles of
dipole-coupled magnetic nanoparticles are theoretically investigated by
performing numerical simulations. The energy landscape of the system is
explored by determining saddle points, adjacent local minima, energy barriers,
and the associated minimum energy paths (MEPs) as functions of the structural
disorder and particle density. The changes in the magnetic order of the
nanostructure along the MEPs connecting adjacent minima are analyzed from a
local perspective. In particular, we determine the extension of the correlated
region where the directions of the particle magnetic moments vary
significantly. It is shown that with increasing degree of disorder the magnetic
correlation range decreases, i.e., the elementary relaxation processes become
more localized. The distribution of the energy barriers, and their relation to
the changes in the magnetic configurations are quantified. Finally, some
implications for the long-time magnetic relaxation dynamics of nanostructures
are discussed.Comment: 19 pages, 6 figure
Phonon-induced quadrupolar ordering of the magnetic superconductor TmNiBC
We present synchrotron x-ray diffraction studies revealing that the lattice
of thulium borocarbide is distorted below T_Q = 13.5 K at zero field. T_Q
increases and the amplitude of the displacements is drastically enhanced, by a
factor of 10 at 60 kOe, when a magnetic field is applied along [100]. The
distortion occurs at the same wave vector as the antiferromagnetic ordering
induced by the a-axis field. A model is presented that accounts for the
properties of the quadrupolar phase and explains the peculiar behavior of the
antiferromagnetic ordering previously observed in this compound.Comment: submitted to PR
Enumeration of self-avoiding walks on the square lattice
We describe a new algorithm for the enumeration of self-avoiding walks on the
square lattice. Using up to 128 processors on a HP Alpha server cluster we have
enumerated the number of self-avoiding walks on the square lattice to length
71. Series for the metric properties of mean-square end-to-end distance,
mean-square radius of gyration and mean-square distance of monomers from the
end points have been derived to length 59. Analysis of the resulting series
yields accurate estimates of the critical exponents and
confirming predictions of their exact values. Likewise we obtain accurate
amplitude estimates yielding precise values for certain universal amplitude
combinations. Finally we report on an analysis giving compelling evidence that
the leading non-analytic correction-to-scaling exponent .Comment: 24 pages, 6 figure
Directed percolation near a wall
Series expansion methods are used to study directed bond percolation clusters
on the square lattice whose lateral growth is restricted by a wall parallel to
the growth direction. The percolation threshold is found to be the same
as that for the bulk. However the values of the critical exponents for the
percolation probability and mean cluster size are quite different from those
for the bulk and are estimated by and respectively. On the other hand the exponent
characterising the scale of the cluster size
distribution is found to be unchanged by the presence of the wall.
The parallel connectedness length, which is the scale for the cluster length
distribution, has an exponent which we estimate to be and is also unchanged. The exponent of the mean
cluster length is related to and by the scaling
relation and using the above estimates
yields to within the accuracy of our results. We conjecture that
this value of is exact and further support for the conjecture is
provided by the direct series expansion estimate .Comment: 12pages LaTeX, ioplppt.sty, to appear in J. Phys.
Dynamic Phases of Vortices in Superconductors with Periodic Pinning
We present results from extensive simulations of driven vortex lattices
interacting with periodic arrays of pinning sites. Changing an applied driving
force produces a rich variety of novel dynamical plastic flow phases which are
very distinct from those observed in systems with random pinning arrays.
Signatures of the transition between these different dynamical phases include
sudden jumps in the current-voltage curves as well as marked changes in the
vortex trajectories and the vortex lattice order. Several dynamical phase
diagrams are obtained as a function of commensurability, pinning strength, and
spatial order of the pinning sites.Comment: 4 pages, 3 figures. To appear in Physical Review Letters. Movies
available at http://www-personal.engin.umich.edu/~nor
Fibrillar templates and soft phases in systems with short-range dipolar and long-range interactions
We analyze the thermal fluctuations of particles that have a short-range
dipolar attraction and a long-range repulsion. In an inhomogeneous particle
density region, or "soft phase," filamentary patterns appear which are
destroyed only at very high temperatures. The filaments act as a fluctuating
template for correlated percolation in which low-energy excitations can move
through the stable pattern by local rearrangements. At intermediate
temperatures, dynamically averaged checkerboard states appear. We discuss
possible implications for cuprate superconducting and related materials.Comment: 4 pages, 4 postscript figures. Discussion of implications for
experiment and theory has been expande
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