344 research outputs found
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
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
A General Limitation on Monte Carlo Algorithms of Metropolis Type
We prove that for any Monte Carlo algorithm of Metropolis type, the
autocorrelation time of a suitable ``energy''-like observable is bounded below
by a multiple of the corresponding ``specific heat''. This bound does not
depend on whether the proposed moves are local or non-local; it depends only on
the distance between the desired probability distribution and the
probability distribution for which the proposal matrix satisfies
detailed balance. We show, with several examples, that this result is
particularly powerful when applied to non-local algorithms.Comment: 8 pages, LaTeX plus subeqnarray.sty (included at end),
NYU-TH-93/07/01, IFUP-TH33/9
Random Walks with Long-Range Self-Repulsion on Proper Time
We introduce a model of self-repelling random walks where the short-range
interaction between two elements of the chain decreases as a power of the
difference in proper time. Analytic results on the exponent are obtained.
They are in good agreement with Monte Carlo simulations in two dimensions. A
numerical study of the scaling functions and of the efficiency of the algorithm
is also presented.Comment: 25 pages latex, 4 postscript figures, uses epsf.sty (all included)
IFUP-Th 13/92 and SNS 14/9
Replica field theory and renormalization group for the Ising spin glass in an external magnetic field
We use the generic replica symmetric cubic field-theory to study the
transition of short range Ising spin glasses in a magnetic field around the
upper critical dimension, d=6. A novel fixed-point is found, in addition to the
well-known zero magnetic field fixed-point, from the application of the
renormalization group. In the spin glass limit, n going to 0, this fixed-point
governs the critical behaviour of a class of systems characterised by a single
cubic interaction parameter. For this universality class, the spin glass
susceptibility diverges at criticality, whereas the longitudinal mode remains
massive. The third mode, the so-called anomalous one, however, behaves
unusually, having a jump at criticality. The physical consequences of this
unusual behaviour are discussed, and a comparison with the conventional de
Almeida-Thouless scenario presented.Comment: 5 pages written in revtex4. Accepted for publication in Phys. Rev.
Let
Improvement of radiopurity level of enriched CdWO and ZnWO crystal scintillators by recrystallization
As low as possible radioactive contamination of a detector plays a crucial
role to improve sensitivity of a double beta decay experiment. The radioactive
contamination of a sample of CdWO crystal scintillator by thorium
was reduced by a factor , down to the level 0.01 mBq/kg
(Th), by exploiting the recrystallization procedure. The total alpha
activity of uranium and thorium daughters was reduced by a factor ,
down to 1.6 mBq/kg. No change in the specific activity (the total
activity and Th) was observed in a sample of ZnWO crystal produced
by recrystallization after removing mm surface layer of the
crystal.Comment: 14 pages, 5 figures and 2 table
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
Zero Temperature Properties of RNA Secondary Structures
We analyze different microscopic RNA models at zero temperature. We discuss
both the most simple model, that suffers a large degeneracy of the ground
state, and models in which the degeneracy has been remove, in a more or less
severe manner. We calculate low-energy density of states using a coupling
perturbing method, where the ground state of a modified Hamiltonian, that
repels the original ground state, is determined. We evaluate scaling exponents
starting from measurements of overlaps and energy differences. In the case of
models without accidental degeneracy of the ground state we are able to clearly
establish the existence of a glassy phase with .Comment: 20 pages including 9 eps figure
Off-equilibrium fluctuation-dissipation relations in the 3d Ising Spin Glass in a magnetic field
We study the fluctuation-dissipation relations for a three dimensional Ising
spin glass in a magnetic field both in the high temperature phase as well as in
the low temperature one. In the region of times simulated we have found that
our results support a picture of the low temperature phase with broken replica
symmetry, but a droplet behavior can not be completely excluded.Comment: 9 pages, 11 ps figures, revtex. Final version to be published in
Phys. Rev.
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