Related papers: Socio-economical dynamics as a solvable spin syste…
We show that the nonequilibrium dynamics of systems with many interacting elements located on a small-world network can be much slower than on regular networks. As an example, we study the phase ordering dynamics of the Ising model on a…
We have composed the ideas of quantum renormalization group and quantum information by exploring the low energy states dynamic of entanglement resources of a system close to its quantum critical point. We demonstrate the low energy states…
We examined energy spectrums of some particular systems of binary spins. It is shown that the configuration space can be divided into classes, and in the limit the energy distributions in these classes can be approximated by the normal…
Biological information processing networks consist of many components, which are coupled by an even larger number of complex multivariate interactions. However, analyses of data sets from fields as diverse as neuroscience, molecular…
In this study the magnetization phenomenon has been investigated as a behavior of interacting elementary moments ensemble, with the help of Ising model [1] in the frame of non-extensive statistical mechanics. To investigate the physical…
Non-reciprocal interactions are a generic feature of non-equilibrium systems. We define a non-reciprocal generalization of the kinetic Ising model in one spatial dimension. We solve the model exactly using two different approaches for…
The nonequilibrium steady state of an infinite-range Ising model is studied. The steady state is obtained by dividing the spins into two groups and attaching them to two heat baths generating spin flips at different temperatures. In the…
An elementary Ising spin model is proposed for demonstrating cascading failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A…
Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a new reliability property, Ising…
Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous…
We propose an information theoretic model for sociological networks. The model is a microcanonical ensemble of states and particles. The states are the possible pairs of nodes (i.e. people, sites and alike) which exchange information. The…
We build simple models for the distribution of voting patterns in a group, using the Supreme Court of the United States as an example. The least structured, or maximum entropy, model that is consistent with the observed pairwise…
This work considers an Ising model on the Apollonian network, where the exchange constant $J_{i,j}\sim1/(k_ik_j)^\mu$ between two neighboring spins $(i,j)$ is a function of the degree $k$ of both spins. Using the exact geometrical…
The nonequilibrium Ising model on a restricted scale-free network has been studied with one- and two-spin flip competing dynamics employing Monte Carlo simulations. The dynamics present in the system can be defined by the probability $q$ in…
Influence maximization in social networks has typically been studied in the context of contagion models and irreversible processes. In this paper, we consider an alternate model that treats individual opinions as spins in an Ising system at…
We study the dynamic and metastable properties of the fully connected Ising $p$-spin model with finite number of variables. We define trapping energies, trapping times and self correlation functions and we analyse their statistical…
In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…
We propose a method to find out the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field $B_s = +\infty$, $B_{t} =…
Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns.…
We study the Ising model on a two-community stochastic block model, where $n$ spins are split into two equal groups with inter-community interaction parameter $\alpha_n\in[0,1]$. We provide a complete characterization of the phase diagram…