Related papers: Network science Ising states of matter
This work maps deep neural networks to classical Ising spin models, allowing them to be described using statistical thermodynamics. The density of states shows that structures emerge in the weights after they have been trained --…
An InfoCGAN neural network is trained on 2-dimensional square Ising configurations conditioned on the external applied magnetic field and the temperature. The network is composed of two main sub-networks. The generator network learns to…
Over the past several years, there have been many studies demonstrating the ability of deep neural networks to identify phase transitions in many physical systems, notably in classical statistical physics systems. One often finds that the…
The Ising model in small-world networks generated from two- and three-dimensional regular lattices has been studied. Monte Carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems. In the…
The Ising model is an equilibrium stochastic process used as a model in several branches of science including magnetic materials, geophysics, neuroscience, sociology and finance. Real systems of interest have finite size and a fixed…
It is well established that neural networks with deep architectures perform better than shallow networks for many tasks in machine learning. In statistical physics, while there has been recent interest in representing physical data with…
We consider Ising model on edge-dual of uncorrelated random networks with arbitrary degree distribution. These networks have a finite clustering in the thermodynamic limit. High and low temperature expansions of Ising model on the edge-dual…
We study the phase transition of the Ising model in networks with core-periphery structures. By Monte Carlo simulations, we show that prior to the order-disorder phase transition the system organizes into an inhomogeneous intermediate phase…
We investigate the efficient learning of magnetic phases using artificial neural networks trained on synthetic data, combining computational simplicity with physics-informed strategies. Focusing on the diluted Ising model, which lacks an…
The two-dimensional (2D) random-bond Ising model has a novel multicritical point on the ferromagnetic to paramagnetic phase boundary. This random phase transition is one of the simplest examples of a 2D critical point occurring at both…
Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it…
The percolation study offers valuable insights into the characteristics of phase transition, shedding light on the underlying mechanisms that govern the formation of global connectivity within the system. We explore the percolation phase…
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…
Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…
We present an analysis of neural network-based machine learning schemes for phases and phase transitions in theoretical condensed matter research, focusing on neural networks with a single hidden layer. Such shallow neural networks were…
We investigate analytically the behavior of Ising model on two connected Barabasi-Albert networks. Depending on relative ordering of both networks there are two possible phases corresponding to parallel or antiparallel alingment of spins in…
The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in…
Multilayer networks provide a framework to study complex systems with multiple types of interactions, multiple dynamical processes, and/or multiple subsystems. When studying a dynamical process on a multilayer network, it is important to…
We demonstrate, by means of a convolutional neural network, that the features learned in the two-dimensional Ising model are sufficiently universal to predict the structure of symmetry-breaking phase transitions in considered systems…
As network research becomes more sophisticated, it is more common than ever for researchers to find themselves not studying a single network but needing to analyze sets of networks. An important task when working with sets of networks is…