4,992 research outputs found
Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions
We present Monte Carlo simulations of the spanning-forest model (q \to 0
limit of the ferromagnetic Potts model) in spatial dimensions d=3,4,5. We show
that, in contrast to the two-dimensional case, the model has a "ferromagnetic"
second-order phase transition at a finite positive value w_c. We present
numerical estimates of w_c and of the thermal and magnetic critical exponents.
We conjecture that the upper critical dimension is 6.Comment: LaTex2e, 4 pages; includes 6 Postscript figures; Version 2 has
expanded title as published in PR
Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm
We study the dynamic critical behavior of the Chayes-Machta dynamics for the
Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang
dynamics for the q-state Potts model to noninteger q, in two and three spatial
dimensions, by Monte Carlo simulation. We show that the Li-Sokal bound z \ge
\alpha/\nu is close to but probably not sharp in d=2, and is far from sharp in
d=3, for all q. The conjecture z \ge \beta/\nu is false (for some values of q)
in both d=2 and d=3.Comment: Revtex4, 4 pages including 4 figure
Cluster simulations of loop models on two-dimensional lattices
We develop cluster algorithms for a broad class of loop models on
two-dimensional lattices, including several standard O(n) loop models at n \ge
1. We show that our algorithm has little or no critical slowing-down when 1 \le
n \le 2. We use this algorithm to investigate the honeycomb-lattice O(n) loop
model, for which we determine several new critical exponents, and a
square-lattice O(n) loop model, for which we obtain new information on the
phase diagram.Comment: LaTex2e, 4 pages; includes 1 table and 2 figures. Totally rewritten
in version 2, with new theory and new data. Version 3 as published in PR
Critical speeding-up in a local dynamics for the random-cluster model
We study the dynamic critical behavior of the local bond-update (Sweeny)
dynamics for the Fortuin-Kasteleyn random-cluster model in dimensions d=2,3, by
Monte Carlo simulation. We show that, for a suitable range of q values, the
global observable S_2 exhibits "critical speeding-up": it decorrelates well on
time scales much less than one sweep, so that the integrated autocorrelation
time tends to zero as the critical point is approached. We also show that the
dynamic critical exponent z_{exp} is very close (possibly equal) to the
rigorous lower bound \alpha/\nu, and quite possibly smaller than the
corresponding exponent for the Chayes-Machta-Swendsen-Wang cluster dynamics.Comment: LaTex2e/revtex4, 4 pages, includes 5 figure
Social Effects in Science: Modelling Agents for a Better Scientific Practice
Science is a fundamental human activity and we trust its results because it
has several error-correcting mechanisms. Its is subject to experimental tests
that are replicated by independent parts. Given the huge amount of information
available, scientists have to rely on the reports of others. This makes it
possible for social effects to influence the scientific community. Here, an
Opinion Dynamics agent model is proposed to describe this situation. The
influence of Nature through experiments is described as an external field that
acts on the experimental agents. We will see that the retirement of old
scientists can be fundamental in the acceptance of a new theory. We will also
investigate the interplay between social influence and observations. This will
allow us to gain insight in the problem of when social effects can have
negligible effects in the conclusions of a scientific community and when we
should worry about them.Comment: 14 pages, 5 figure
Grassmann Integral Representation for Spanning Hyperforests
Given a hypergraph G, we introduce a Grassmann algebra over the vertex set,
and show that a class of Grassmann integrals permits an expansion in terms of
spanning hyperforests. Special cases provide the generating functions for
rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All
these results are generalizations of Kirchhoff's matrix-tree theorem.
Furthermore, we show that the class of integrals describing unrooted spanning
(hyper)forests is induced by a theory with an underlying OSP(1|2)
supersymmetry.Comment: 50 pages, it uses some latex macros. Accepted for publication on J.
Phys.
Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0
We simulate self-avoiding walks on a cubic lattice and determine the second
virial coefficient for walks of different lengths. This allows us to determine
the critical value of the renormalized four-point coupling constant in the
three-dimensional N-vector universality class for N=0. We obtain g* =
1.4005(5), where g is normalized so that the three-dimensional
field-theoretical beta-function behaves as \beta(g) = - g + g^2 for small g. As
a byproduct, we also obtain precise estimates of the interpenetration ratio
Psi*, Psi* = 0.24685(11), and of the exponent \nu, \nu = 0.5876(2).Comment: 16 page
Fractal Characterizations of MAX Statistical Distribution in Genetic Association Studies
Two non-integer parameters are defined for MAX statistics, which are maxima
of simpler test statistics. The first parameter, , is the
fractional number of tests, representing the equivalent numbers of independent
tests in MAX. If the tests are dependent, . The second
parameter is the fractional degrees of freedom of the chi-square
distribution that fits the MAX null distribution. These two
parameters, and , can be independently defined, and can be
non-integer even if is an integer. We illustrate these two parameters
using the example of MAX2 and MAX3 statistics in genetic case-control studies.
We speculate that is related to the amount of ambiguity of the model
inferred by the test. In the case-control genetic association, tests with low
(e.g. ) are able to provide definitive information about the disease
model, as versus tests with high (e.g. ) that are completely uncertain
about the disease model. Similar to Heisenberg's uncertain principle, the
ability to infer disease model and the ability to detect significant
association may not be simultaneously optimized, and seems to measure the
level of their balance
Failure of vaccination to prevent outbreaks of foot-and-mouth disease
Outbreaks of foot-and-mouth disease persist in dairy cattle herds in Saudi Arabia despite revaccination at intervals of 4-6 months. Vaccine trials provide data on antibody responses following vaccination. Using this information we developed a mathematical model of the decay of protective antibodies with which we estimated the fraction of susceptible animals at a given time after vaccination. The model describes the data well, suggesting over 95% take with an antibody half-life of 43 days. Farm records provided data on the time course of five outbreaks. We applied a 'SLIR' epidemiological model to these data, fitting a single parameter representing disease transmission rate. The analysis provides estimates of the basic reproduction number R(0), which may exceed 70 in some cases. We conclude that the critical intervaccination interval which would provide herd immunity against FMDV is unrealistically short, especially for heterologous challenge. We suggest that it may not be possible to prevent foot-and-mouth disease outbreaks on these farms using currently available vaccines
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