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]
The prototypical example of a spin chain is the Heisenberg model, described by Werner Heisenberg in 1928. [1] This models a one-dimensional lattice of fixed particles with spin 1/2. A simple version (the antiferromagnetic XXX model) was solved, that is, the spectrum of the Hamiltonian of the Heisenberg model was determined, by Hans Bethe using ...
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.
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.
One can immediately find if is restricted to 1 only, the Hamiltonian reduces to conventional Heisenberg model. An important feature of the multipolar exchange Hamiltonian is its anisotropy. [ 21 ] The value of coupling constant C K i K j Q i Q j {\displaystyle C_{K_{i}K_{j}}^{Q{i}Q_{j}}} is usually very sensitive to the relative angle between ...
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.