Search results
Results from the WOW.Com Content Network
The J1–J2 model is a quantum spin model like the Heisenberg model but also includes a term for the interaction between next-nearest neighbor spins.
It is common to name the model depending on the values of , and : if , the model is called the Heisenberg XYZ model; in the case of = = =, it is the Heisenberg XXZ model; if = = =, it is the Heisenberg XXX model. The spin 1/2 Heisenberg model in one dimension may be solved exactly using the Bethe ansatz. [1]
This equation is called the continuous classical Heisenberg ferromagnet equation or, more shortly, the Heisenberg model and is integrable in the sense of soliton theory. It admits several integrable and nonintegrable generalizations like the Landau-Lifshitz equation , the Ishimori equation , and so on.
For instance, the Ising model describes spins (dipoles) that have only two possible states, up and down, whereas in the Heisenberg model the spin vector is allowed to point in any direction. In certain magnets, the magnetic dipoles are only free to rotate in a 2D plane, a system which can be adequately described by the so-called xy-model.
Heisenberg model can refer to two models in statistical mechanics: Heisenberg model (classical) , a classical nearest neighbour spin model Heisenberg model (quantum) , a model where the spins are treated quantum mechanically using Pauli matrices
The Majumdar–Ghosh model is defined by the following Hamiltonian: ^ = = + + = + where the S vector is a quantum spin operator with quantum number S = 1/2.. Other conventions for the coefficients may be taken in the literature, but the most important fact is that the ratio of first-neighbor to second-neighbor couplings is 2 to 1.
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more
Heisenberg went on to say that Born and Jordan's contribution to quantum mechanics cannot be changed by "a wrong decision from the outside". [28] In 1954, Heisenberg wrote an article honoring Max Planck for his insight in 1900. In the article, Heisenberg credited Born and Jordan for the final mathematical formulation of matrix mechanics and ...