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The ferromagnetic transition in the Ising model is the paradigmatic example of ergodicity breaking accompanied by symmetry breaking. It is routinely assumed that the thermodynamic limit is taken with free or periodic boundary conditions.…
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…
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 --…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
The study of nonequilibrium steady-state (NESS) in the Ising model offers rich insights into the properties of complex systems far from equilibrium. This paper explores the nature of NESS phase transitions in two-dimensional (2D)…
Despite the general acknowledgment of the role of niche and fitness differences in community dynamics, species abundance has been coined as a relevant feature not just regarding niche perspectives, but also according to neutral…
We study numerically the region above the critical temperature of the four dimensional Random Field Ising Model. Using a cluster dynamic we measure the connected and disconnected magnetic susceptibility and the connected and disconnected…
Properties of nanoparticles have been studied within the framework of Ising model and the method of random-field interactions: the average magnetic moment and position of critical points of the magnetic and the concentration phase…
We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter $m$ through the restricted free energy…
The metastable lifetime of the square-lattice and simple-cubic-lattice kinetic Ising models are studied in the low-temperature limit. The simulations are performed using Monte Carlo with Absorbing Markov Chain algorithms to simulate…
We investigate the stochastic resonance phenomena in the field-driven Ising model on small-world networks. The response of the magnetization to an oscillating magnetic field is examined by means of Monte Carlo dynamic simulations, with the…
The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising model is studied at zero-temperature. A single characteristic length scale, $L(t)$, is extracted from the equal time correlation function. In the pure case, the…
By studying numerically the phase-ordering kinetics of a two-dimensional ferromagnetic Ising model with quenched disorder -- either random bonds or random fields -- we show that a critical percolation structure forms in an early stage and…
A relation between a class of stationary points of the energy landscape of continuous spin models on a lattice and the configurations of a Ising model defined on the same lattice suggests an approximate expression for the microcanonical…
We investigate the final state of zero-temperature Ising ferromagnets which are endowed with single-spin flip Glauber dynamics. Surprisingly, the ground state is generally not reached for zero initial magnetization. In two dimensions, the…
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…
We study the equilibrium and dynamic phase transition properties of two-dimensional Ising model on a decorated triangular lattice under the influence of a time-dependent magnetic field composed of a periodic square wave part plus a time…
We study the dynamical response of a two-dimensional Ising model subject to a square-wave oscillating external field. In contrast to earlier studies, the system evolves under a so-called soft Glauber dynamic [P.A. Rikvold and M. Kolesik, J.…
Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for…
We study both analytically and numerically metastability and nucleation in a two-dimensional nonequilibrium Ising ferromagnet. Canonical equilibrium is dynamically impeded by a weak random perturbation which models homogeneous disorder of…