Related papers: Critical Exponents for Diluted Resistor Networks
Within the framework of the renormalization group approach to the models of critical dynamics, we propose a method for a considerable reduction of the number of integrals needed to calculate the critical exponents. With this method we…
The self-consistent probabilistic approach has proven itself powerful in studying the percolation behavior of interdependent or multiplex networks without tracking the percolation process through each cascading step. In order to understand…
The thermal-to-percolative crossover exponent \phi, well-known for ferromagnetic systems, is studied extensively for Edwards-Anderson spin glasses. The scaling of defect energies are determined at the bond percolation threshold p_c, using…
We calculate the surface critical exponents of the ordinary transition occuring in semi-infinite, quenched dilute Ising-like systems. This is done by applying the field theoretic approach directly in d=3 dimensions up to the two-loop…
An order parameter description of the Anderson-Mott transition (AMT) is given. We first derive an order parameter field theory for the AMT, and then present a mean-field solution. It is shown that the mean-field critical exponents are exact…
We propose a statistical model defined on the three-dimensional diamond network where the splitting of randomly selected nodes leads to a spatially disordered network, with decreasing degree of connectivity. The terminal state, that is…
Strain-controlled criticality governs the elasticity of jamming and fiber networks. While the upper critical dimension of jamming is believed to be $d_u$=2, non mean-field exponents are observed in numerical studies of 2D and 3D fiber…
We study the current flow paths between two edges in a random resistor network on a $L\times L$ square lattice. Each resistor has resistance $e^{ax}$, where $x$ is a uniformly-distributed random variable and $a$ controls the broadness of…
We develop a field-theoretic representation for the configurations of an interface between two ordered phases of a q-state Potts model in two dimensions, in the solid-on-solid approximation. The model resembles the field theory of directed…
We give an analogy between non-reversible Markov chains and electric networks much in the flavour of the classical reversible results originating from Kakutani, and later Kem\'eny-Snell-Knapp and Kelly. Non-reversibility is made possible by…
Our goal is to study statistical properies of "dielectric resonances" which are poles of conductance of a large random $LC$ network. Such poles are a particular example of eigenvalues $\lambda_n$ of matrix pencils ${\bf H}-\lambda {\bf W}$,…
We present new evaluation of the critical exponents of O(n)- symmetric \phi^4 theory from the field theoretical renormalization group, based on the new algorithm for summing divergent series. The central values practically coincide with…
In this short note we derive Mott's law for the critical conductance of the Miller-Abrahams random resistor network on a Poisson point process on $\mathbb{R}^d$, $d\geq 2$, and we give a percolative characterization of the factor preceding…
Mean field theory has been successfully used to analyze deep neural networks (DNN) in the infinite size limit. Given the finite size of realistic DNN, we utilize the large deviation theory and path integral analysis to study the deviation…
We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…
I use a previously introduced mapping between the continuum percolation model and the Potts fluid to derive a mean field theory of continuum percolation systems. This is done by introducing a new variational principle, the basis of which…
Networks composed from both connectivity and dependency links were found to be more vulnerable compared to classical networks with only connectivity links. Their percolation transition is usually of a first order compared to the second…
The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transition and make it difficult to predict the critical point of…
Modern network systems, such as transportation and communication systems, are prone to cyber-physical disruptions and thus suffer efficiency loss. This paper studies network resiliency, in terms of throughput, and develops resilient control…
We present a field-theoretical treatment of the critical behavior of three-dimensional weakly diluted quenched Ising model. To this end we analyse in a replica limit n=0 5-loop renormalization group functions of the $\phi^4$-theory with…