Related papers: Origins of the Ising model
The life of Ernst Ising and the steps to solving the model named after him are reported in parallel. Wilhelm Lenz suggested his student Ernst Ising to explain the existence of ferromagnetism on the basis of his publication in 1920. The…
On this, the occasion of the 20th anniversary of the "Ising Lectures" in Lviv (Ukraine), we give some personal reflections about the famous model that was suggested by Wilhelm Lenz for ferromagnetism in 1920 and solved in one dimension by…
We take the occasion of this article to review one hundred years of the physical and mathematical study of the Ising model. The model, introduced by Lenz in 1920, has been at the cornerstone of many major revolutions in statistical…
Today, the Ising model is an archetype describing collective ordering processes. And, as such, it is widely known in physics and far beyond. Less known is the fact that the thesis defended by Ernst Ising 100 years ago (in 1924) contained…
The Lenz-Ising model has served for almost a century as a basis for understanding ferromagnetism, and has become a paradigmatic model for phase transitions in statistical mechanics. While retaining the Ising energy arguments, we use…
A longstanding problem in natural science and later in physics was the understanding of the existence of ferromagnetism and its disappearance under heating to high temperatures. Although a qualitative description was possible by the…
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 two-dimensional Ising model of a ferromagnet allows for many ways of computing its partition function and other properties. Each way reveals surprising features of what we might call Ising Matter. Moreover, the various ways would appear…
The Ising model is famous model for magnetic substances in Statistical Physics, and has been greatly studied in many forms. It was solved in one-dimension by Ernst Ising in 1925 and in two-dimensions without an external magnetic field by…
The one-dimensional Ising model in an external magnetic field with uniform long-range interactions and random short-range interactions satisfying bimodal annealed distributions is studied. This generalizes the random model discussed by…
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…
We examine in detail the theoretical foundations of striking long-range couplings emerging in arrays of fluid cells connected by narrow channels by using a lattice gas (Ising model) description of a system. We present a reexamination of the…
Following Fr\"ohlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+\alpha}$, $0\leq \alpha\leq 1/2$. We introduce a geometric description of the spin…
This chapter provides a general introduction of network modeling in psychometrics. The chapter starts with an introduction to the statistical model formulation of pairwise Markov random fields (PMRF), followed by an introduction of the PMRF…
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…
We have considered the $S=1/2$ antiferromagnetic Heisenberg model in two dimensions, with an additional Ising \nnn interaction. Antiferromagnetic \nnn interactions will lead to frustration, and the system responds with flipping the spins…
We consider an Ising model where longitudinal components of every pair of spins have antiferromagnetic interaction of the same magnitude. When subjected to a transverse magnetic field at zero temperature, the system undergoes a phase…
We study numerically the ordering kinetics in a two-dimensional Ising model with random coupling where the fraction of antiferromagnetic links $a$ can be gradually tuned. We show that, upon increasing such fraction, the behavior changes in…
The Ashkin-Teller model is a pair of interacting Ising models and has two parameters: $J$ is a coupling constant in the Ising models and $U$ describes the strength of the interaction between them. In the ferromagnetic case $J,U>0$ on the…
We consider the ferromagnetic Ising model on a highly inhomogeneous network created by a growth process. We find that the phase transition in this system is characterised by the Berezinskii--Kosterlitz--Thouless singularity, although…