Related papers: Magnetisation and mean field theory in the Ising m…
Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between…
We construct an exactly solvable circuit of interacting memristors and study its dynamics and fixed points. This simple circuit model interpolates between decoupled circuits of isolated memristors, and memristors in series, for which exact…
We analyze in some detail a recently proposed transfer matrix mean field approximation which yields the exact critical point for several two dimensional nearest neighbor Ising models. For the square lattice model we show explicitly that…
We study the stationary properties of the Ising model that, while evolving towards its equilibrium state at temperature $T$ according to the Glauber dynamics, is stochastically reset to its fixed initial configuration with magnetisation…
We compare dynamic mean-field and dynamic cavity as methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and compare to the exact…
In this work 2D Ising systems were used to simulate the reversals of the Earth's magnetic field. Each spin was supposed to be a ring current in the Earth dynamo and the magnetization to be proportional to the field intensity. Given the…
We performed two-dimensional simulated tempering (ST) simulations of the two-dimensional Ising model with different lattice sizes in order to investigate the two-dimensional ST's applicability to dealing with phase transitions and to study…
We consider the mean field theory of the Random Field Ising Model obtained by weighing the many solutions of the mean field equations with Boltzmann-like factors. These solutions are found numerically in three dimensions and we observe…
In this paper the exact solution and correlation functions for a double-chain Ising model with multi-spin interactions and symmetric Hamiltonian density are obtained. The study employs the transfer matrix method to derive fundamental…
We investigate the statistics of the mean magnetisation, of its large deviations and persistent large deviations in simple coarsening systems. We consider more specifically the case of the diffusion equation, of the Ising chain at zero…
In this paper, we investigate the dynamics of the two-dimensional Ising model with stochastic resetting, utilizing a constant resetting rate procedure with zero-strength initial magnetization. Our results reveal the presence of a…
An entropy of the Ising model in the mean field approximation is derived by the Hamilton-Jacobi formalism. We consider a grand canonical ensemble with respect to the temperature and the external magnetic field. A cusp arises at the critical…
We use representation theory to write a formula for the magnetisation of the quantum Heisenberg ferromagnet. The core new result is a spectral decomposition of the function $\alpha_k 2^{\alpha_1+\dotsb+\alpha_n}$ where $\alpha_k$ is the…
The emergence of complex modulated structures in the magnetization pattern of thin films is a well-established experimental phenomenology caused by the frustrating effects of competing interactions. Using a coarse-grained version of the…
We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The…
Mean-field galactic dynamo theory is the leading theory to explain the prevalence of regular magnetic fields in spiral galaxies, but its systematic comparison with observations is still incomplete and fragmentary. Here we compare…
We construct a natural coupling between the continuum Gaussian free field (GFF) and the critical Ising magnetisation field (IMF) in a planar domain. In fact, we show that two independent IMFs with $+$ boundary conditions and two independent…
Using the density-matrix renormalization-group method we study the surface critical behaviour of the magnetization in Ising strips in the subcritical region. Our results support the prediction that the surface magnetization in the two…
The mean field approximation to the Ising model is a canonical variational tool that is used for analysis and inference in Ising models. We provide a simple and optimal bound for the KL error of the mean field approximation for Ising models…
As first asserted by Y. Imry and S-K Ma, the famed discontinuity of the magnetization as function of the magnetic field in the two dimensional Ising model is eliminated, for all temperatures, through the addition of quenched random magnetic…