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 ?
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?
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).
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.
Chapter 4 focuses on the two-dimensional Ising model and the various accounts of the thermodynamical properties and behaviour exhibited by the lattice of spins.
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.
This is the goal of this proposal, which is organized in three objectives:(I) Build a deep correspondence between the Ising model and CFT: reveal clear links between the objects and structures arising in the Ising and CFT frameworks.
Among their topics are the multifractal analysis of irregularities and scaling in signal and image processing, from fractional Browning motion to multifractional and multistable motion, watching the markets misbehave, Mandelbrot as an educator, the long-range dependence of the two-dimensional Ising model at critical temperature, Mandelbrot in finance, the entropic origins of allometry relations, music and fractals, and stories about Benoit.