Ising model


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Ising model

A model which consists of a lattice of “spin” variables with two characteristic properties: (1) each of the spin variables independently takes on either the value +1 or the value -1; and (2) only pairs of nearest-neighboring spins can interact. The study of this model in two dimensions forms the basis of the modern theory of phase transitions and, more generally, of cooperative phenomena.

A macroscopic piece of material consists of a large number of atoms, the number being of the order of the Avogadro number (approximately 6 × 1023). Thermodynamic phenomena all depend on the participation of such a large number of atoms. Even though the fundamental interaction between atoms is short-ranged, the presence of this large number of atoms can, under suitable conditions, lead to an effective interaction between widely separated atoms. Phenomena due to such effective long-range interactions are referred to as cooperative phenomena. The simplest examples of cooperative phenomena are phase transitions. The most familiar phase transition is either the condensation of steam into water or the freezing of water into ice. Only slightly less familiar is the ferromagnetic phase transition that takes place at the Curie temperature, which, for example, is roughly 1043 K for iron. See Curie temperature, Ferromagnetism, Phase transitions

Ising model

[′ī·ziŋ ‚mäd·əl]
(solid-state physics)
A crude model of a ferromagnetic material or an analogous system, used to study phase transitions, in which atoms in a one-, two-, or three-dimensional lattice interact via Ising coupling between nearest neighbors, and the spin components of the atoms are coupled to a uniform magnetic field.
References in periodicals archive ?
(2) Tadashi Kadowaki and Hidetoshi Nishimori, "Quantum annealing in the transverse Ising model," Physical Review E, Nov.
In particular, the Ising model describes spins ("compass needles") constrained to point either up or down, perpendicular to the plane.
Gulpinar investigated the critical behavior of ultrasound wave absorption coefficient in the metamagnetic Ising model within the mean-field approximation [38].
Based on the Ising model, this paper combines the influence among users and the influence of social environment, that is, describing the decision-making behavior of users in the process of spreading rumors in the medium and macroaspects.
Here we use a quantum simulator composed of up to 53 qubits to study non-equilibrium dynamics in the transverse-field Ising model with long-range interactions."
Specific topics include the signed mean curvature measure, discrete holomorphicity and Ising model operator formalism, scaling asymptotics of heat kernels of line bundles, the topology of Dolbeault cohomology groups, and the point source inverse back-scatter problem.
Why are some models, like the harmonic oscillator, the Ising model, a few Hamiltonian equations in quantum mechanics, the Poisson equation, or the Lokta-Volterra equations, repeatedly used within and across scientific domains, whereas theories allow for many more modeling possibilities?
By utilizing a measure that maximizes entropy, which can be applied with the information regarding neuronal correlations, we obtain a Bayesian model called the Ising model [14] and a method of decoding neuronal ensemble activity based on this model is called the Ising decoder [12].
In 2D even the simplest models, such as the Ising model, lead to the correlation functions for which we do not have explicit analytical expressions making them virtually useless for our purposes.
The Ising model involves discrete variables [s.sub.i] (spins) placed on a sampling grid.
In Section 6 we find a specialization of the initial variables under which urban renewal becomes the Ising Y-[DELTA] transformation, which is a transformation of the Ising model changing the interaction strengths in a different way from how they change under the resistor network Y-[DELTA] transformation, but changing the graph in exactly the same way.
Ghliyem, Mixed spin Ising model with four-spin interaction and random crystal field, Physica B: 407, 6-13 (2012).