90 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
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
Islanding the power grid on the transmission level: less connections for more security
Islanding is known as a management procedure of the power system that is implemented at the distribution level to preserve sensible loads from outages and to guarantee the continuity in electricity supply, when a high amount of distributed generation occurs. In this paper we study islanding on the level of the transmission grid and shall show that it is a suitable measure to enhance energy security and grid resilience. We consider the German and Italian transmission grids. We remove links either randomly to mimic random failure events, or according to a topological characteristic, their so-called betweenness centrality, to mimic an intentional attack and test whether the resulting fragments are self-sustainable. We test this option via the tool of optimized DC power flow equations. When transmission lines are removed according to their betweenness centrality, the resulting islands have a higher chance of being dynamically self-sustainable than for a random removal. Less connections may even increase the grid’s stability. These facts should be taken into account in the design of future power grids
- …