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

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

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

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