234 research outputs found
A derivative formula for the free energy function
We consider bond percolation on the lattice. Let be the
number of open clusters in . It is well known that converges to the free energy function at the zero field.
In this paper, we show that converges to
.Comment: 8 pages 1 figur
Broken scaling in the Forest Fire Model
We investigate the scaling behavior of the cluster size distribution in the
Drossel-Schwabl Forest Fire model (DS-FFM) by means of large scale numerical
simulations, partly on (massively) parallel machines. It turns out that simple
scaling is clearly violated, as already pointed out by Grassberger [P.
Grassberger, J. Phys. A: Math. Gen. 26, 2081 (1993)], but largely ignored in
the literature. Most surprisingly the statistics not seems to be described by a
universal scaling function, and the scale of the physically relevant region
seems to be a constant. Our results strongly suggest that the DS-FFM is not
critical in the sense of being free of characteristic scales.Comment: 9 pages in RevTEX4 format (9 figures), submitted to PR
Conductivity of 2D many-component electron gas, partially-quantized by magnetic field
The 2D semimetal consisting of heavy holes and light electrons is studied.
The consideration is based on assumption that electrons are quantized by
magnetic field while holes remain classical. We assume also that the
interaction between components is weak and the conversion between components is
absent. The kinetic equation for holes colliding with quantized electrons is
utilized. It has been stated that the inter-component friction and
corresponding correction to the dissipative conductivity {\it do
not vanish at zero temperature} due to degeneracy of the Landau levels. This
correction arises when the Fermi level crosses the Landau level.
The limits of kinetic equation applicability were found. We also study the
situation of kinetic memory when particles repeatedly return to the points of
their meeting.Comment: 13 pages, 1 figur
Site Percolation and Phase Transitions in Two Dimensions
The properties of the pure-site clusters of spin models, i.e. the clusters
which are obtained by joining nearest-neighbour spins of the same sign, are
here investigated. In the Ising model in two dimensions it is known that such
clusters undergo a percolation transition exactly at the critical point. We
show that this result is valid for a wide class of bidimensional systems
undergoing a continuous magnetization transition. We provide numerical evidence
for discrete as well as for continuous spin models, including SU(N) lattice
gauge theories. The critical percolation exponents do not coincide with the
ones of the thermal transition, but they are the same for models belonging to
the same universality class.Comment: 8 pages, 6 figures, 2 tables. Numerical part developed; figures,
references and comments adde
Specific Heat Exponent for the 3-d Ising Model from a 24-th Order High Temperature Series
We compute high temperature expansions of the 3-d Ising model using a
recursive transfer-matrix algorithm and extend the expansion of the free energy
to 24th order. Using ID-Pade and ratio methods, we extract the critical
exponent of the specific heat to be alpha=0.104(4).Comment: 10 pages, LaTeX with 5 eps-figures using epsf.sty, IASSNS-93/83 and
WUB-93-4
Planar lattice gases with nearest-neighbour exclusion
We discuss the hard-hexagon and hard-square problems, as well as the
corresponding problem on the honeycomb lattice. The case when the activity is
unity is of interest to combinatorialists, being the problem of counting binary
matrices with no two adjacent 1's. For this case we use the powerful corner
transfer matrix method to numerically evaluate the partition function per site,
density and some near-neighbour correlations to high accuracy. In particular
for the square lattice we obtain the partition function per site to 43 decimal
places.Comment: 16 pages, 2 built-in Latex figures, 4 table
Magnetoresistance of Three-Constituent Composites: Percolation Near a Critical Line
Scaling theory, duality symmetry, and numerical simulations of a random
network model are used to study the magnetoresistance of a
metal/insulator/perfect conductor composite with a disordered columnar
microstructure. The phase diagram is found to have a critical line which
separates regions of saturating and non-saturating magnetoresistance. The
percolation problem which describes this line is a generalization of
anisotropic percolation. We locate the percolation threshold and determine the
t = s = 1.30 +- 0.02, nu = 4/3 +- 0.02, which are the same as in
two-constituent 2D isotropic percolation. We also determine the exponents which
characterize the critical dependence on magnetic field, and confirm numerically
that nu is independent of anisotropy. We propose and test a complete scaling
description of the magnetoresistance in the vicinity of the critical line.Comment: Substantially revised version; description of behavior in finite
magnetic fields added. 7 pages, 7 figures, submitted to PR
Percolation on two- and three-dimensional lattices
In this work we apply a highly efficient Monte Carlo algorithm recently
proposed by Newman and Ziff to treat percolation problems. The site and bond
percolation are studied on a number of lattices in two and three dimensions.
Quite good results for the wrapping probabilities, correlation length critical
exponent and critical concentration are obtained for the square, simple cubic,
HCP and hexagonal lattices by using relatively small systems. We also confirm
the universal aspect of the wrapping probabilities regarding site and bond
dilution.Comment: 15 pages, 6 figures, 3 table
The Ising Susceptibility Scaling Function
We have dramatically extended the zero field susceptibility series at both
high and low temperature of the Ising model on the triangular and honeycomb
lattices, and used these data and newly available further terms for the square
lattice to calculate a number of terms in the scaling function expansion around
both the ferromagnetic and, for the square and honeycomb lattices, the
antiferromagnetic critical point.Comment: PDFLaTeX, 50 pages, 5 figures, zip file with series coefficients and
background data in Maple format provided with the source files. Vs2: Added
dedication and made several minor additions and corrections. Vs3: Minor
corrections. Vs4: No change to eprint. Added essential square-lattice series
input data (used in the calculation) that were removed from University of
Melbourne's websit
Extension to order of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices
Using a renormalized linked-cluster-expansion method, we have extended to
order the high-temperature series for the susceptibility
and the second-moment correlation length of the spin-1/2 Ising models on
the sc and the bcc lattices. A study of these expansions yields updated direct
estimates of universal parameters, such as exponents and amplitude ratios,
which characterize the critical behavior of and . Our best
estimates for the inverse critical temperatures are
and . For the
susceptibility exponent we get and for the correlation
length exponent we get .
The ratio of the critical amplitudes of above and below the critical
temperature is estimated to be . The analogous ratio for
is estimated to be . For the correction-to-scaling
amplitude ratio we obtain .Comment: Misprints corrected, 8 pages, latex, no figure
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