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 ?
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?
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.
In section 6 we show how superurban renewal specializes to the Y-Delta transformation for the Ising model.
He provides commentaries to introduce each topic, which include Dimer statistics, duality and gauge transformations, the Ising model, the Potts model, critical frontiers, percolation, graph theory, and knot invariants.
9:30 HYSTERESIS LOOP AREA OF THE KINETIC ISING MODEL WITH NEXT-NEAREST NEIGHBOR INTERACTION, William D.
The result is related to the Ising model and to results obtained for nonclassical diffusion obeying a diffusion equation of fractional order in time.
They were interested in simulating the so-called Ising model, which features an abrupt, temperature-dependent transition from an ordered to a disordered state in a system in which neighboring particles have either the same or opposite spins.
In preparation for simulating the three-dimensional Ising model, Ferrenberg tested this package on the two-dimensional version, which has a known answer.
There are some very notable examples of such behaviour, for instance, the subcritical Ising model, see [4; 15] and references therein, as well as the discussion in Section 3.
For [beta] [greater than or equal to] 0, the Ising model on the graph G with parameter [beta] is the probability measure [pi] on S given by
The remaining two chapters consider the general setting for Gibbs measures, and the application of the Ising model to log Sobolev inequalities to show the stabilization of the Glauber-Langevin dynamic.
This work presents original research on continuum quantum geometric path integrals applied to Yang-Mills theory and variants, such as QCD, Chern-Simons theory, and Ising Models.