3,040 research outputs found
Field theory of Ising percolating clusters
The clusters of up spins of a two-dimensional Ising ferromagnet undergo a
second order percolative transition at temperatures above the Curie point. We
show that in the scaling limit the percolation threshold is described by an
integrable field theory and identify the non-perturbative mechanism which
allows the percolative transition in absence of thermodynamic singularities.
The analysis is extended to the Kertesz line along which the Coniglio-Klein
droplets percolate in a positive magnetic field.Comment: 19 pages, 8 figure
Decentralized Maximum Likelihood Estimation for Sensor Networks Composed of Nonlinearly Coupled Dynamical Systems
In this paper we propose a decentralized sensor network scheme capable to
reach a globally optimum maximum likelihood (ML) estimate through
self-synchronization of nonlinearly coupled dynamical systems. Each node of the
network is composed of a sensor and a first-order dynamical system initialized
with the local measurements. Nearby nodes interact with each other exchanging
their state value and the final estimate is associated to the state derivative
of each dynamical system. We derive the conditions on the coupling mechanism
guaranteeing that, if the network observes one common phenomenon, each node
converges to the globally optimal ML estimate. We prove that the synchronized
state is globally asymptotically stable if the coupling strength exceeds a
given threshold. Acting on a single parameter, the coupling strength, we show
how, in the case of nonlinear coupling, the network behavior can switch from a
global consensus system to a spatial clustering system. Finally, we show the
effect of the network topology on the scalability properties of the network and
we validate our theoretical findings with simulation results.Comment: Journal paper accepted on IEEE Transactions on Signal Processin
Matrix elements of the operator T\bar{T} in integrable quantum field theory
Recently A. Zamolodchikov obtained a series of identities for the expectation
values of the composite operator T\bar{T} constructed from the components of
the energy-momentum tensor in two-dimensional quantum field theory. We show
that if the theory is integrable the addition of a requirement of factorization
at high energies can lead to the exact determination of the generic matrix
element of this operator on the asymptotic states. The construction is
performed explicitly in the Lee-Yang model.Comment: 22 pages, one reference adde
The composite operator T\bar{T} in sinh-Gordon and a series of massive minimal models
The composite operator T\bar{T}, obtained from the components of the
energy-momentum tensor, enjoys a quite general characterization in
two-dimensional quantum field theory also away from criticality. We use the
form factor bootstrap supplemented by asymptotic conditions to determine its
matrix elements in the sinh-Gordon model. The results extend to the breather
sector of the sine-Gordon model and to the minimal models M_{2/(2N+3)}
perturbed by the operator phi_{1,3}.Comment: 29 page
Universal amplitude ratios in the two-dimensional Ising model
We use the results of integrable field theory to determine the universal
amplitude ratios in the two-dimensional Ising model. In particular, the exact
values of the ratios involving amplitudes computed at nonzero magnetic field
are provided.Comment: 9 pages; a factor 8/15 included in the amplitude A_c and the ratio
R_A, typos correcte
Phase separation and interface structure in two dimensions from field theory
We study phase separation in two dimensions in the scaling limit below
criticality. The general form of the magnetization profile as the volume goes
to infinity is determined exactly within the field theoretical framework which
explicitly takes into account the topological nature of the elementary
excitations. The result known for the Ising model from its lattice solution is
recovered as a particular case. In the asymptotic infrared limit the interface
behaves as a simple curve characterized by a gaussian passage probability
density. The leading deviation, due to branching, from this behavior is also
derived and its coefficient is determined for the Potts model. As a byproduct,
for random percolation we obtain the asymptotic density profile of a spanning
cluster conditioned to touch only the left half of the boundary.Comment: 12 pages, 3 figures; published version, references adde
Distributed Decision Through Self-Synchronizing Sensor Networks in the Presence of Propagation Delays and Nonreciprocal Channels
In this paper we propose and analyze a distributed algorithm for achieving
globally optimal decisions, either estimation or detection, through a
self-synchronization mechanism among linearly coupled integrators initialized
with local measurements. We model the interaction among the nodes as a directed
graph with weights dependent on the radio interface and we pose special
attention to the effect of the propagation delays occurring in the exchange of
data among sensors, as a function of the network geometry. We derive necessary
and sufficient conditions for the proposed system to reach a consensus on
globally optimal decision statistics. One of the major results proved in this
work is that a consensus is achieved for any bounded delay condition if and
only if the directed graph is quasi-strongly connected. We also provide a
closed form expression for the global consensus, showing that the effect of
delays is, in general, to introduce a bias in the final decision. The closed
form expression is also useful to modify the consensus mechanism in order to
get rid of the bias with minimum extra complexity.Comment: Conference paper. Journal version submitted to IEEE Transactions on
Signal Processing, January 10, 2007. Paper accepted for the publication on
the VIII IEEE Workshop on Signal Processing Advances in Wireless
Communications, (SPAWC 2007), January 22, 200
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