Related papers: Ising models on the Regularized Apollonian Network
The universal critical point ratio $Q$ is exploited to determine positions of the critical Ising transition lines on the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the ratio $Q$ in the…
A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model…
Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a…
Spin systems have emerged as powerful tools for understanding collective phenomena in complex systems. In this work, we investigate the Ashkin--Teller (AT) model on random scale-free networks using mean-field theory, which extends the…
We consider phase separation on the strip for the two-dimensional Ising model in the near-critical region. Within the framework of field theory, we find exact analytic results for certain two- and three-point correlation functions of the…
We numerically study bootstrap percolation on Kleinberg's spatial networks, in which the probability density function of a node to have a long-range link at distance $r$ scales as $P(r)\sim r^{\alpha}$. Setting the ratio of the size of the…
Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks…
A coarse-grained description of the restricted primitive model is considered in terms of the local charge- and number-density fields. Exact reduction to a one-field theory is derived, and exact expressions for the number-density correlation…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
We introduce a family of random matrices where correlations between matrix elements are induced via interaction-derived Boltzmann factors. Varying these yields access to different ensembles. We find a universal scaling behavior of the…
We analyze the ferromagnetic Ising model on a scale-free tree; the growing random network model with the linear attachment kernel $A_k=k+\alpha$ introduced by [Krapivsky et al.: Phys. Rev. Lett. {\bf 85} (2000) 4629-4632]. We derive an…
The paper investigates nonlinear system identification using system output data at various linearized operating points. A feed-forward multi-layer Artificial Neural Network (ANN) based approach is used for this purpose and tested for two…
When interfaces between ordered domains are ordered clusters, frustration disappears. A phase with mixed ordered structures emerges but no length scale can be associated to. We show that sum of densities of each structure plays the role of…
Embeddings are one of the fundamental building blocks for data analysis tasks. Embeddings are already essential tools for large language models and image analysis, and their use is being extended to many other research domains. The…
The $q$-neighbor Ising model for the opinion formation on multiplex networks with two layers in the form of random graphs (duplex networks), the partial overlap of nodes, and LOCAL\&AND spin update rule was investigated by means of the pair…
We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality…
The antiferromagnetic Ising model in uncorrelated scale-free networks has been studied by means of Monte Carlo simulations. These networks are characterized by a connectivity (or degree) distribution P(k) ~ k^(- gamma). The disorder present…
Analytic phenomenological scaling is carried out for the random field Ising model in general dimensions using a bar geometry. Domain wall configurations and their decorated profiles and associated wandering and other exponents…
An Ising model with ferromagnetic nearest-neighbor interactions $J_{1}$ ($J_{1}>0$) and random next-nearest-neighbor interactions [$+J_{2}$ with probability $p$ and $-J_{2}$ with probability $(1-p)$; $J_{2}>0$] is studied within the…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…