11,708 research outputs found
The F model on dynamical quadrangulations
The dynamically triangulated random surface (DTRS) approach to Euclidean
quantum gravity in two dimensions is considered for the case of the elemental
building blocks being quadrangles instead of the usually used triangles. The
well-known algorithmic tools for treating dynamical triangulations in a Monte
Carlo simulation are adapted to the problem of these dynamical
quadrangulations. The thus defined ensemble of 4-valent graphs is appropriate
for coupling to it the 6- and 8-vertex models of statistical mechanics. Using a
series of extensive Monte Carlo simulations and accompanying finite-size
scaling analyses, we investigate the critical behaviour of the 6-vertex F model
coupled to the ensemble of dynamical quadrangulations and determine the matter
related as well as the graph related critical exponents of the model.Comment: LaTeX, 43 pages, 10 figures, 7 tables; substantially shortened and
revised version as published, for more details refer to V1, to be found at
http://arxiv.org/abs/hep-lat/0409028v
Directed paths on hierarchical lattices with random sign weights
We study sums of directed paths on a hierarchical lattice where each bond has
either a positive or negative sign with a probability . Such path sums
have been used to model interference effects by hopping electrons in the
strongly localized regime. The advantage of hierarchical lattices is that they
include path crossings, ignored by mean field approaches, while still
permitting analytical treatment. Here, we perform a scaling analysis of the
controversial ``sign transition'' using Monte Carlo sampling, and conclude that
the transition exists and is second order. Furthermore, we make use of exact
moment recursion relations to find that the moments always determine,
uniquely, the probability distribution $P(J)$. We also derive, exactly, the
moment behavior as a function of $p$ in the thermodynamic limit. Extrapolations
($n\to 0$) to obtain for odd and even moments yield a new signal for
the transition that coincides with Monte Carlo simulations. Analysis of high
moments yield interesting ``solitonic'' structures that propagate as a function
of . Finally, we derive the exact probability distribution for path sums
up to length L=64 for all sign probabilities.Comment: 20 pages, 12 figure
A periodic elastic medium in which periodicity is relevant
We analyze, in both (1+1)- and (2+1)- dimensions, a periodic elastic medium
in which the periodicity is such that at long distances the behavior is always
in the random-substrate universality class. This contrasts with the models with
an additive periodic potential in which, according to the field theoretic
analysis of Bouchaud and Georges and more recently of Emig and Nattermann, the
random manifold class dominates at long distances in (1+1)- and
(2+1)-dimensions. The models we use are random-bond Ising interfaces in
hypercubic lattices. The exchange constants are random in a slab of size
and these coupling constants are periodically repeated
along either {10} or {11} (in (1+1)-dimensions) and {100} or {111} (in
(2+1)-dimensions). Exact ground-state calculations confirm scaling arguments
which predict that the surface roughness behaves as: and , with in
-dimensions and; and , with in -dimensions.Comment: Submitted to Phys. Rev.
High-Temperature Series Expansions for Random Potts Models
We discuss recently generated high-temperature series expansions for the free
energy and the susceptibility of random-bond q-state Potts models on hypercubic
lattices. Using the star-graph expansion technique quenched disorder averages
can be calculated exactly for arbitrary uncorrelated coupling distributions
while keeping the disorder strength p as well as the dimension d as symbolic
parameters. We present analyses of the new series for the susceptibility of the
Ising (q=2) and 4-state Potts model in three dimensions up to order 19 and 18,
respectively, and compare our findings with results from field-theoretical
renormalization group studies and Monte Carlo simulations.Comment: 16 pages,cmp209.sty (included), 9 postscript figures, author
information under http://www.physik.uni-leipzig.de/index.php?id=2
Universal features of information spreading efficiency on -dimensional lattices
A model for information spreading in a population of mobile agents is
extended to -dimensional regular lattices. This model, already studied on
two-dimensional lattices, also takes into account the degeneration of
information as it passes from one agent to the other. Here, we find that the
structure of the underlying lattice strongly affects the time at which
the whole population has been reached by information. By comparing numerical
simulations with mean-field calculations, we show that dimension is
marginal for this problem and mean-field calculations become exact for .
Nevertheless, the striking nonmonotonic behavior exhibited by the final degree
of information with respect to and the lattice size appears to be
geometry independent.Comment: 8 pages, 9 figure
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