255 research outputs found
The problem of predecessors on spanning trees
We consider the equiprobable distribution of spanning trees on the square
lattice. All bonds of each tree can be oriented uniquely with respect to an
arbitrary chosen site called the root. The problem of predecessors is finding
the probability that a path along the oriented bonds passes sequentially fixed
sites and . The conformal field theory for the Potts model predicts the
fractal dimension of the path to be 5/4. Using this result, we show that the
probability in the predecessors problem for two sites separated by large
distance decreases as . If sites and are
nearest neighbors on the square lattice, the probability can be
found from the analytical theory developed for the sandpile model. The known
equivalence between the loop erased random walk (LERW) and the directed path on
the spanning tree says that is the probability for the LERW started at
to reach the neighboring site . By analogy with the self-avoiding walk,
can be called the return probability. Extensive Monte-Carlo simulations
confirm the theoretical predictions.Comment: 7 pages, 2 figure
Critical Dynamics of Self-Organizing Eulerian Walkers
The model of self-organizing Eulerian walkers is numerically investigated on
the square lattice. The critical exponents for the distribution of a number of
steps () and visited sites () characterizing the process of
transformation from one recurrent configuration to another are calculated using
the finite-size scaling analysis. Two different kinds of dynamical rules are
considered. The results of simulations show that both the versions of the model
belong to the same class of universality with the critical exponents
.Comment: 3 pages, 4 Postscript figures, RevTeX, additional information
available at http://thsun1.jinr.dubna.su/~shche
Non-Local Finite-Size Effects in the Dimer Model
We study the finite-size corrections of the dimer model on
square lattice with two different boundary conditions: free and periodic. We
find that the finite-size corrections depend in a crucial way on the parity of
, and show that, because of certain non-local features present in the model,
a change of parity of induces a change of boundary condition. Taking a
careful account of this, these unusual finite-size behaviours can be fully
explained in the framework of the logarithmic conformal field theory.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium
on Non-Perturbative and Symmetry Methods in Field Theory (June 2006,
Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Exact solution of the Bernoulli matching model of sequence alignment
Through a series of exact mappings we reinterpret the Bernoulli model of
sequence alignment in terms of the discrete-time totally asymmetric exclusion
process with backward sequential update and step function initial condition.
Using earlier results from the Bethe ansatz we obtain analytically the exact
distribution of the length of the longest common subsequence of two sequences
of finite lengths . Asymptotic analysis adapted from random matrix theory
allows us to derive the thermodynamic limit directly from the finite-size
result.Comment: 13 pages, 4 figure
Exact velocity of dispersive flow in the asymmetric avalanche process
Using the Bethe ansatz we obtain the exact solution for the one-dimensional
asymmetric avalanche process. We evaluate the velocity of dispersive flow as a
function of driving force and the density of particles. The obtained solution
shows a dynamical transition from intermittent to continuous flow.Comment: 12 page
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