1,514 research outputs found
Lattice Green Function (at 0) for the 4d Hypercubic Lattice
The generating function for recurrent Polya walks on the four dimensional
hypercubic lattice is expressed as a Kampe-de-Feriet function. Various
properties of the associated walks are enumerated.Comment: latex, 5 pages, Res. Report 1
Role of conformational entropy in force-induced bio-polymer unfolding
A statistical mechanical description of flexible and semi-flexible polymer
chains in a poor solvent is developed in the constant force and constant
distance ensembles. We predict the existence of many intermediate states at low
temperatures stabilized by the force. A unified response to pulling and
compressing forces has been obtained in the constant distance ensemble. We show
the signature of a cross-over length which increases linearly with the chain
length. Below this cross-over length, the critical force of unfolding decreases
with temperature, while above, it increases with temperature. For stiff chains,
we report for the first time "saw-tooth" like behavior in the force-extension
curves which has been seen earlier in the case of protein unfolding.Comment: 4 pages, 5 figures, ReVTeX4 style. Accepted in Phys. Rev. Let
Universal Amplitude Combinations for Self-Avoiding Walks, Polygons and Trails
We give exact relations for a number of amplitude combinations that occur in
the study of self-avoiding walks, polygons and lattice trails. In particular,
we elucidate the lattice-dependent factors which occur in those combinations
which are otherwise universal, show how these are modified for oriented
lattices, and give new results for amplitude ratios involving even moments of
the area of polygons. We also survey numerical results for a wide range of
amplitudes on a number of oriented and regular lattices, and provide some new
ones.Comment: 20 pages, NI 92016, OUTP 92-54S, UCSBTH-92-5
Wither the sliding Luttinger liquid phase in the planar pyrochlore
Using series expansion based on the flow equation method we study the zero
temperature properties of the spin-1/2 planar pyrochlore antiferromagnet in the
limit of strong diagonal coupling. Starting from the limit of decoupled crossed
dimers we analyze the evolution of the ground state energy and the elementary
triplet excitations in terms of two coupling constants describing the inter
dimer exchange. In the limit of weakly coupled spin-1/2 chains we find that the
fully frustrated inter chain coupling is critical, forcing a dimer phase which
adiabatically connects to the state of isolated dimers. This result is
consistent with findings by O. Starykh, A. Furusaki and L. Balents (Phys. Rev.
B 72, 094416 (2005)) which is inconsistent with a two-dimensional sliding
Luttinger liquid phase at finite inter chain coupling.Comment: 6 pages, 4 Postscript figures, 1 tabl
High-temperature expansions through order 24 for the two-dimensional classical XY model on the square lattice
The high-temperature expansion of the spin-spin correlation function of the
two-dimensional classical XY (planar rotator) model on the square lattice is
extended by three terms, from order 21 through order 24, and analyzed to
improve the estimates of the critical parameters.Comment: 7 pages, 2 figure
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
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
Statistics of lattice animals (polyominoes) and polygons
We have developed an improved algorithm that allows us to enumerate the
number of site animals (polyominoes) on the square lattice up to size 46.
Analysis of the resulting series yields an improved estimate, , for the growth constant of lattice animals and confirms to a very
high degree of certainty that the generating function has a logarithmic
divergence. We prove the bound We also calculate the radius
of gyration of both lattice animals and polygons enumerated by area. The
analysis of the radius of gyration series yields the estimate , for both animals and polygons enumerated by area. The mean
perimeter of polygons of area is also calculated. A number of new amplitude
estimates are given.Comment: 10 pages, 2 eps figure
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