107 research outputs found
Dynamical linke cluster expansions: Algorithmic aspects and applications
Dynamical linked cluster expansions are linked cluster expansions with
hopping parameter terms endowed with their own dynamics. They amount to a
generalization of series expansions from 2-point to point-link-point
interactions. We outline an associated multiple-line graph theory involving
extended notions of connectivity and indicate an algorithmic implementation of
graphs. Fields of applications are SU(N) gauge Higgs systems within variational
estimates, spin glasses and partially annealed neural networks. We present
results for the critical line in an SU(2) gauge Higgs model for the electroweak
phase transition. The results agree well with corresponding high precision
Monte Carlo results.Comment: LATTICE98(algorithms
Finite Size Scaling Analysis with Linked Cluster Expansions
Linked cluster expansions are generalized from an infinite to a finite volume
on a -dimensional hypercubic lattice. They are performed to 20th order in
the expansion parameter to investigate the phase structure of scalar
models for the cases of and in 3 dimensions. In particular we
propose a new criterion to distinguish first from second order transitions via
the volume dependence of response functions for couplings close to but not at
the critical value. The criterion is applicable to Monte Carlo simulations as
well. Here it is used to localize the tricritical line in a
theory. We indicate further applications to the electroweak transition.Comment: 3 pages, 1 figure, Talk presented at LATTICE96(Theoretical
Developments
Order-by-disorder in classical oscillator systems
We consider classical nonlinear oscillators on hexagonal lattices. When the
coupling between the elements is repulsive, we observe coexisting states, each
one with its own basin of attraction. These states differ by their degree of
synchronization and by patterns of phase-locked motion. When disorder is
introduced into the system by additive or multiplicative Gaussian noise, we
observe a non-monotonic dependence of the degree of order in the system as a
function of the noise intensity: intervals of noise intensity with low
synchronization between the oscillators alternate with intervals where more
oscillators are synchronized. In the latter case, noise induces a higher degree
of order in the sense of a larger number of nearly coinciding phases. This
order-by-disorder effect is reminiscent to the analogous phenomenon known from
spin systems. Surprisingly, this non-monotonic evolution of the degree of order
is found not only for a single interval of intermediate noise strength, but
repeatedly as a function of increasing noise intensity. We observe noise-driven
migration of oscillator phases in a rough potential landscape.Comment: 12 pages, 13 figures; comments are welcom
Chiral Symmetry Restoration at Finite Temperature in the Linear Sigma--Model
The temperature behaviour of meson condensates
is calculated in the -linear sigma model. The couplings of
the Lagrangian are fitted to the physical masses, the pion
decay constant and a scalar mass of GeV. The quartic
terms of the mesonic interaction are converted to a quadratic term with the
help of a Hubbard-Stratonovich transformation. Effective mass terms are
generated this way, which are treated self-consistently to leading order of a
-expansion. We calculate the light and strange -quark condensates using PCAC relations between the meson masses and
condensates. For a cut-off value of 1.5 GeV we find a first-order chiral
transition at a critical temperature MeV. At this temperature the
spontaneously broken subgroup is restored. Entropy density,
energy density and pressure are calculated for temperatures up to and slightly
above the critical temperature. To our surprise we find some indications for a
reduced contribution from strange mesons for .Comment: 17 pages, HD--TVP--93--15. (3 figures - available on request
Simulation of Consensus Model of Deffuant et al on a Barabasi-Albert Network
In the consensus model with bounded confidence, studied by Deffuant et al.
(2000), two randomly selected people who differ not too much in their opinion
both shift their opinions towards each other. Now we restrict this exchange of
information to people connected by a scale-free network. As a result, the
number of different final opinions (when no complete consensus is formed) is
proportional to the number of people.Comment: 7 pages including 3 figs; Int.J.MOd.Phys.C 15, issue 2; programming
error correcte
Pair-factorized steady states on arbitrary graphs
Stochastic mass transport models are usually described by specifying hopping
rates of particles between sites of a given lattice, and the goal is to predict
the existence and properties of the steady state. Here we ask the reverse
question: given a stationary state that factorizes over links (pairs of sites)
of an arbitrary connected graph, what are possible hopping rates that converge
to this state? We define a class of hopping functions which lead to the same
steady state and guarantee current conservation but may differ by the induced
current strength. For the special case of anisotropic hopping in two dimensions
we discuss some aspects of the phase structure. We also show how this case can
be traced back to an effective zero-range process in one dimension which is
solvable for a large class of hopping functions.Comment: IOP style, 9 pages, 1 figur
Stochastic Description of a Bistable Frustrated Unit
Mixed positive and negative feedback loops are often found in biological
systems which support oscillations. In this work we consider a prototype of
such systems, which has been recently found at the core of many genetic
circuits showing oscillatory behaviour. Our model consists of two interacting
species A and B, where A activates not only its own production, but also that
of its repressor B. While the self-activation of A leads already to a bistable
unit, the coupling with a negative feedback loop via B makes the unit
frustrated. In the deterministic limit of infinitely many molecules, such a
bistable frustrated unit is known to show excitable and oscillatory dynamics,
depending on the maximum production rate of A which acts as a control
parameter. We study this model in its fully stochastic version and we find
oscillations even for parameters which in the deterministic limit are deeply in
the fixed-point regime. The deeper we go into this regime, the more irregular
these oscillations are, becoming finally random excitations whenever
fluctuations allow the system to overcome the barrier for a large excursion in
phase space. The fluctuations can no longer be fully treated as a perturbation.
The smaller the system size (the number of molecules), the more frequent are
these excitations. Therefore, stochasticity caused by demographic noise makes
this unit even more flexible with respect to its oscillatory behaviour.Comment: 28 pages, 17 figure
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