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J1 J2 Model
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. Hamiltonian In this model, the term J_1 represents the usual nearest-neighbor interaction as seen in the Heisenberg model, and J_2 represents the exchange interaction to the ''next'' nearest-neighbor. : \hat H = J_1 \sum_\vec S_i \cdot \vec S_j + J_2 \sum_ \vec S_i \cdot \vec S_j See also *Spin model *Heisenberg model (quantum) *Hubbard model *t-J model *Majumdar–Ghosh model The Majumdar–Ghosh model is a one-dimensional quantum Heisenberg spin model in which the nearest-neighbour antiferromagnetic exchange interaction is twice as strong as the next-nearest-neighbour interaction. It is a special case of the more gen ... References * * * * *{{cite journal, last1=Majumdar, first1=Chanchal K., last2=Ghosh, first2=Dipan K., title=On Next‐Nearest‐Neighbor Interaction in Linear Chain. II, journal=Journal of Mathematical Physics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Spin Model
A spin model is a mathematical model used in physics primarily to explain magnetism. Spin models may either be classical or quantum mechanical in nature. Spin models have been studied in quantum field theory as examples of integrable models. Spin models are also used in quantum information theory and computability theory in theoretical computer science. The theory of spin models is a far reaching and unifying topic that cuts across many fields. Introduction In ordinary materials, the magnetic dipole moments of individual atoms produce magnetic fields that cancel one another, because each dipole points in a random direction. Ferromagnetic materials below their Curie temperature, however, exhibit magnetic domains in which the atomic dipole moments are locally aligned, producing a macroscopic, non-zero magnetic field from the domain. These are the ordinary "magnets" with which we are all familiar. The study of the behavior of such "spin models" is a thriving area of research in con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heisenberg Model (quantum)
The quantum Heisenberg model, developed by Werner Heisenberg, is a statistical mechanical model used in the study of critical points and phase transitions of magnetic systems, in which the spins of the magnetic systems are treated quantum mechanically. It is related to the prototypical Ising model, where at each site of a lattice, a spin \sigma_i \in \ represents a microscopic magnetic dipole to which the magnetic moment is either up or down. Except the coupling between magnetic dipole moments, there is also a multipolar version of Heisenberg model called the multipolar exchange interaction. Overview For quantum mechanical reasons (see exchange interaction or ), the dominant coupling between two dipoles may cause nearest-neighbors to have lowest energy when they are ''aligned''. Under this assumption (so that magnetic interactions only occur between adjacent dipoles) and on a 1-dimensional periodic lattice, the Hamiltonian can be written in the form :\hat H = -J \sum_^ \sig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin Model
A spin model is a mathematical model used in physics primarily to explain magnetism. Spin models may either be classical or quantum mechanical in nature. Spin models have been studied in quantum field theory as examples of integrable models. Spin models are also used in quantum information theory and computability theory in theoretical computer science. The theory of spin models is a far reaching and unifying topic that cuts across many fields. Introduction In ordinary materials, the magnetic dipole moments of individual atoms produce magnetic fields that cancel one another, because each dipole points in a random direction. Ferromagnetic materials below their Curie temperature, however, exhibit magnetic domains in which the atomic dipole moments are locally aligned, producing a macroscopic, non-zero magnetic field from the domain. These are the ordinary "magnets" with which we are all familiar. The study of the behavior of such "spin models" is a thriving area of research in con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hubbard Model
The Hubbard model is an approximate model used to describe the transition between conducting and insulating systems. It is particularly useful in solid-state physics. The model is named for John Hubbard. The Hubbard model states that each electron experiences competing forces: one pushes it to tunnel to neighboring atoms, while the other pushes it away from its neighbors. Its Hamiltonian thus has two terms: a kinetic term allowing for tunneling ("hopping") of particles between lattice sites and a potential term reflecting on-site interaction. The particles can either be fermions, as in Hubbard's original work, or bosons, in which case the model is referred to as the "Bose–Hubbard model". The Hubbard model is a useful approximation for particles in a periodic potential at sufficiently low temperatures, where all the particles may be assumed to be in the lowest Bloch band, and long-range interactions between the particles can be ignored. If interactions between particles at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T-J Model
In solid-state physics, the ''t''-''J'' model is a model first derived in 1977 from the Hubbard model by Józef Spałek to explain antiferromagnetic properties of the Mott insulators and taking into account experimental results about the strength of electron-electron repulsion in this materials. The model consider the materials as a lattice with atoms in the knots (sites) and just one or two external electrons moving among them (internal electrons are not considered), like in the basic Hubbard model. That difference is in supposing electrons being strongly-correlated, that means electrons are very sensible to reciprocal coulombic repulsion, and so are more constrained to avoid occupying lattice's sites already occupied by another electron. In the basic Hubbard model, the repulsion, indicated with ''U'', can be small and also null, and electrons are freer to jump (''hopping'', parametrized by ''t'' as ''transfer'' or ''tunnel'') from one site to another. In the ''t''-''J'' mode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majumdar–Ghosh Model
The Majumdar–Ghosh model is a one-dimensional quantum Heisenberg spin model in which the nearest-neighbour antiferromagnetic exchange interaction is twice as strong as the next-nearest-neighbour interaction. It is a special case of the more general J_1-J_2 model, with J_1=2J_2. The model is named after Indian physicists Chanchal Kumar Majumdar and Dipan Ghosh. The Majumdar–Ghosh model is notable because its ground states (lowest energy quantum states) can be found exactly and written in a simple form, making it a useful starting point for understanding more complex spin models and phases. Definition The Majumdar–Ghosh model is defined by the following Hamiltonian: :\hat H = J \sum_^ \vec_j \cdot \vec_ + \frac \sum_^ \vec_j \cdot\vec_ 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin Models
Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally biased portrayal of something Spin, spinning or spinnin may also refer to: Physics and mathematics * Spin, the rotation of an object around a central axis * Spin (physics) or particle spin, a fundamental property of elementary particles * Spin group, a particular double cover of the special orthogonal group SO(''n'') * Spin tensor, a tensor quantity for describing spinning motion in special relativity and general relativity * Spin (aerodynamics), autorotation of an aerodynamically stalled aeroplane * SPIN bibliographic database, an indexing and abstracting service focusing on physics research Textile arts * Spinning (polymers), a process for creating polymer fibres * Spinning (textiles), the creation of yarn or thread by twistin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
