3,297 research outputs found
Probability distribution of residence times of grains in models of ricepiles
We study the probability distribution of residence time of a grain at a site,
and its total residence time inside a pile, in different ricepile models. The
tails of these distributions are dominated by the grains that get deeply buried
in the pile. We show that, for a pile of size , the probabilities that the
residence time at a site or the total residence time is greater than , both
decay as for where
is an exponent , and values of and in the two
cases are different. In the Oslo ricepile model we find that the probability
that the residence time at a site being greater than or equal to ,
is a non-monotonic function of for a fixed and does not obey simple
scaling. For model in dimensions, we show that the probability of minimum
slope configuration in the steady state, for large , varies as where is a constant, and hence .Comment: 13 pages, 23 figures, Submitted to Phys. Rev.
Exact entropy of dimer coverings for a class of lattices in three or more dimensions
We construct a class of lattices in three and higher dimensions for which the
number of dimer coverings can be determined exactly using elementary arguments.
These lattices are a generalization of the two-dimensional kagome lattice, and
the method also works for graphs without translational symmetry. The partition
function for dimer coverings on these lattices can be determined also for a
class of assignments of different activities to different edges.Comment: 4 pages, 2 figures; added results on partition function when
different edges have different weights; modified abstract; added reference
Percolation Systems away from the Critical Point
This article reviews some effects of disorder in percolation systems even
away from the critical density p_c. For densities below p_c, the statistics of
large clusters defines the animals problem. Its relation to the directed
animals problem and the Lee-Yang edge singularity problem is described. Rare
compact clusters give rise to Griffiths singuraties in the free energy of
diluted ferromagnets, and lead to a very slow relaxation of magnetization. In
biassed diffusion on percolation clusters, trapping in dead-end branches leads
to asymptotic drift velocity becoming zero for strong bias, and very slow
relaxation of velocity near the critical bias field.Comment: Minor typos fixed. Submitted to Praman
On the orientational ordering of long rods on a lattice
We argue that a system of straight rigid rods of length k on square lattice
with only hard-core interactions shows two phase transitions as a function of
density, rho, for k >= 7. The system undergoes a phase transition from the
low-density disordered phase to a nematic phase as rho is increased from 0, at
rho = rho_c1, and then again undergoes a reentrant phase transition from the
nematic phase to a disordered phase at rho = rho_c2 < 1.Comment: epl.cl
Work distribution functions for hysteresis loops in a single-spin system
We compute the distribution of the work done in driving a single Ising spin
with a time-dependent magnetic field. Using Glauber dynamics we perform
Monte-Carlo simulations to find the work distributions at different driving
rates. We find that in general the work-distributions are broad with a
significant probability for processes with negative dissipated work. The
special cases of slow and fast driving rates are studied analytically. We
verify that various work fluctuation theorems corresponding to equilibrium
initial states are satisfied while a steady state version is not.Comment: 9 pages, 15 figure
Tailoring symmetry groups using external alternate fields
Macroscopic systems with continuous symmetries subjected to oscillatory
fields have phases and transitions that are qualitatively different from their
equilibrium ones. Depending on the amplitude and frequency of the fields
applied, Heisenberg ferromagnets can become XY or Ising-like -or, conversely,
anisotropies can be compensated -thus changing the nature of the ordered phase
and the topology of defects. The phenomena can be viewed as a dynamic form of
"order by disorder".Comment: 4 pages, 2 figures finite dimension and selection mechanism clarifie
Rolling tachyon solution of two-dimensional string theory
We consider a classical (string) field theory of matrix model which was
developed earlier in hep-th/9207011 and subsequent papers. This is a
noncommutative field theory where the noncommutativity parameter is the string
coupling . We construct a classical solution of this field theory and show
that it describes the complete time history of the recently found rolling
tachyon on an unstable D0 brane.Comment: 19 pages, 2 figures, minor changes in text and additional references,
correction of decay time (version to appear in JHEP.
Distribution of sizes of erased loops of loop-erased random walks in two and three dimensions
We show that in the loop-erased random walk problem, the exponent
characterizing probability distribution of areas of erased loops is
superuniversal. In d-dimensions, the probability that the erased loop has an
area A varies as A^{-2} for large A, independent of d, for 2 <= d <= 4. We
estimate the exponents characterizing the distribution of perimeters and areas
of erased loops in d = 2 and 3 by large-scale Monte Carlo simulations. Our
estimate of the fractal dimension z in two-dimensions is consistent with the
known exact value 5/4. In three-dimensions, we get z = 1.6183 +- 0.0004. The
exponent for the distribution of durations of avalanche in the
three-dimensional abelian sandpile model is determined from this by using
scaling relations.Comment: 25 pages, 1 table, 8 figure
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