24,434 research outputs found
Vanishing of Gravitational Particle Production in the Formation of Cosmic Strings
We consider the gravitationally induced particle production from the quantum
vacuum which is defined by a free, massless and minimally coupled scalar field
during the formation of a gauge cosmic string. Previous discussions of this
topic estimate the power output per unit length along the string to be of the
order of ergs/sec/cm in the s-channel. We find that this production
may be completely suppressed. A similar result is also expected to hold for the
number of produced photons.Comment: 10 pages, Plain LaTex. Minor improvements. To appear in PR
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
Perimeter Generating Functions For The Mean-Squared Radius Of Gyration Of Convex Polygons
We have derived long series expansions for the perimeter generating functions
of the radius of gyration of various polygons with a convexity constraint.
Using the series we numerically find simple (algebraic) exact solutions for the
generating functions. In all cases the size exponent .Comment: 8 pages, 1 figur
A new transfer-matrix algorithm for exact enumerations: Self-avoiding polygons on the square lattice
We present a new and more efficient implementation of transfer-matrix methods
for exact enumerations of lattice objects. The new method is illustrated by an
application to the enumeration of self-avoiding polygons on the square lattice.
A detailed comparison with the previous best algorithm shows significant
improvement in the running time of the algorithm. The new algorithm is used to
extend the enumeration of polygons to length 130 from the previous record of
110.Comment: 17 pages, 8 figures, IoP style file
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
Osculating and neighbour-avoiding polygons on the square lattice
We study two simple modifications of self-avoiding polygons. Osculating
polygons are a super-set in which we allow the perimeter of the polygon to
touch at a vertex. Neighbour-avoiding polygons are only allowed to have nearest
neighbour vertices provided these are joined by the associated edge and thus
form a sub-set of self-avoiding polygons. We use the finite lattice method to
count the number of osculating polygons and neighbour-avoiding polygons on the
square lattice. We also calculate their radius of gyration and the first
area-weighted moment. Analysis of the series confirms exact predictions for the
critical exponents and the universality of various amplitude combinations. For
both cases we have found exact solutions for the number of convex and
almost-convex polygons.Comment: 14 pages, 5 figure
Hard hexagon partition function for complex fugacity
We study the analyticity of the partition function of the hard hexagon model
in the complex fugacity plane by computing zeros and transfer matrix
eigenvalues for large finite size systems. We find that the partition function
per site computed by Baxter in the thermodynamic limit for positive real values
of the fugacity is not sufficient to describe the analyticity in the full
complex fugacity plane. We also obtain a new algebraic equation for the low
density partition function per site.Comment: 49 pages, IoP styles files, lots of figures (png mostly) so using
PDFLaTeX. Some minor changes added to version 2 in response to referee
report
Integrability vs non-integrability: Hard hexagons and hard squares compared
In this paper we compare the integrable hard hexagon model with the
non-integrable hard squares model by means of partition function roots and
transfer matrix eigenvalues. We consider partition functions for toroidal,
cylindrical, and free-free boundary conditions up to sizes and
transfer matrices up to 30 sites. For all boundary conditions the hard squares
roots are seen to lie in a bounded area of the complex fugacity plane along
with the universal hard core line segment on the negative real fugacity axis.
The density of roots on this line segment matches the derivative of the phase
difference between the eigenvalues of largest (and equal) moduli and exhibits
much greater structure than the corresponding density of hard hexagons. We also
study the special point of hard squares where all eigenvalues have unit
modulus, and we give several conjectures for the value at of the
partition functions.Comment: 46 page
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