Related papers: On Testing for Parameters in Ising Models
Activated transitions have rates that are often exponentially small in system size. Extracting the associated activation barriers is challenging in practice, especially in the deeply metastable regimes and in the presence of disorder. Here,…
We show using extensive simulation results and physical arguments that an Ising system on a two dimensional square lattice, having interactions of random sign between first neighbors and ferromagnetic interactions between second neighbors,…
We contribute to the mathematical theory of the design of low temperature Ising machines, a type of experimental probabilistic computing device implementing the Ising model. Encoding the output of a function in the ground state of a…
The phase diagram of the random field Ising model on the Bethe lattice with a symmetric dichotomous random field is closely investigated with respect to the transition between the ferromagnetic and paramagnetic regime. Refining arguments of…
The Ising model is a celebrated example of a Markov random field, introduced in statistical physics to model ferromagnetism. This is a discrete exponential family with binary outcomes, where the sufficient statistic involves a quadratic…
We provide a rigorous microscopic derivation of the thermodynamic description of equilibrium crystal shapes in the presence of a substrate, first studied by Winterbottom. We consider finite range ferromagnetic Ising models with pair…
The Ising antiferromagnets on the triangular and on the pyrochlore lattices are two of the most iconic examples of magnetic frustration, paradigmatically illustrating many exotic properties such as emergent gauge fields, fractionalisation,…
We study minimax rates for denoising simultaneously sparse and low rank matrices in high dimensions. We show that an iterative thresholding algorithm achieves (near) optimal rates adaptively under mild conditions for a large class of loss…
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…
The four dimensional Gaussian random field Ising magnet is investigated numerically at zero temperature, using samples up to size $64^4$, to test scaling theories and to investigate the nature of domain walls and the thermodynamic limit. As…
We report the results of the magnetisation reversal in Ising ferromagnet having thermal and field gradients by Monte Carlo simulation. We have studied the distribution of reversal times for different values of thermal and field gradients…
The performance of data fusion and tracking algorithms often depends on parameters that not only describe the sensor system, but can also be task-specific. While for the sensor system tuning these variables is time-consuming and mostly…
In this paper, we consider the Ising model on random $d$-regular graphs (with $d\ge3$) and Erd\"os-R\'enyi graphs $G(n,d/n)$ (with $d>1$) at the critical temperature. We prove that the \textit{magnetization}, i.e.\ the sum of the spins of a…
We study two-dimensional ferromagnetic Ising model on a series of regular lattices, which are represented as the tessellation of polygons with p>=5 sides, such as pentagons (p=5), hexagons (p=6), etc. Such lattices are on hyperbolic planes,…
The two-dimensional Ising model with competing short range ferromagnetic interactions and long range antiferromagnetic interactions is perhaps the most simple one containing the minimal microscopic ingredients necessary for an appropriate…
The sparse signal processing literature often uses random sensing matrices to obtain performance guarantees. Unfortunately, in the real world, sensing matrices do not always come from random processes. It is therefore desirable to evaluate…
We demonstrate the applicability of the $\epsilon$-convergence algorithm in extracting the critical temperatures and critical exponents of three-dimensional Ising models. We analyze the low temperature magnetization as well as high…
We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\lambda$, in a scaling…
We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…
We construct periodic approximations to the free energies of Ising models on fractal lattices of dimension smaller than two, in the case of zero external magnetic field, using a generalization of the combinatorial method of Feynman and…