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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] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and heat capacity—in terms of microscopic parameters that fluctuate about average values and are characterized by probability distributions. This established the fields of statistical thermodynamics and statistical physics. The founding of the field of statistical mechanics is generally credited to three physicists: *Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates *James Clerk Maxwell, who developed models of probability distr ... [...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] |
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] |
Ising Model
The Ising model () (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors. Neighboring spins that agree have a lower energy than those that disagree; the system tends to the lowest energy but heat disturbs this tendency, thus creating the possibility of different structural phases. The model allows the identification of phase transitions as a simplified model of reality. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition. The Ising model was invented by the physicist , who gave it as a prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Heisenberg Model (classical)
The Classical Heisenberg model, developed by Werner Heisenberg, is the n = 3 case of the n-vector model, one of the models used in statistical physics to model ferromagnetism, and other phenomena. Definition It can be formulated as follows: take a d-dimensional lattice, and a set of spins of the unit length :\vec_i \in \mathbb^3, , \vec_i, =1\quad (1), each one placed on a lattice node. The model is defined through the following Hamiltonian: : \mathcal = -\sum_ \mathcal_ \vec_i \cdot \vec_j\quad (2) with : \mathcal_ = \begin J & \mboxi, j\mbox \\ 0 & \mbox\end a coupling between spins. Properties * The general mathematical formalism used to describe and solve the Heisenberg model and certain generalizations is developed in the article on the Potts model. * In the continuum limit the Heisenberg model (2) gives the following equation of motion :: \vec_=\vec\wedge \vec_. :This equation is called the continuous classical Heisenberg ferromagnet equation or shortly Heisenberg model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AKLT Model
The AKLT model is an extension of the one-dimensional quantum Heisenberg spin model. The proposal and exact solution of this model by Ian Affleck, Elliott H. Lieb, Tom Kennedy and provided crucial insight into the physics of the spin-1 Heisenberg chain. It has also served as a useful example for such concepts as valence bond solid order, symmetry-protected topological order and matrix product state wavefunctions. Background A major motivation for the AKLT model was the Majumdar–Ghosh chain. Because two out of every set of three neighboring spins in a Majumdar–Ghosh ground state are paired into a singlet, or valence bond, the three spins together can never be found to be in a spin 3/2 state. In fact, the Majumdar–Ghosh Hamiltonian is nothing but the sum of all projectors of three neighboring spins onto a 3/2 state. The main insight of the AKLT paper was that this construction could be generalized to obtain exactly solvable models for spin sizes other than 1/2. Just ... [...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] |
Valence Bond Solid
Valence or valency may refer to: Science * Valence (chemistry), a measure of an element's combining power with other atoms * Degree (graph theory), also called the valency of a vertex in graph theory * Valency (linguistics), aspect of verbs relative to other parts of speech * Valence (psychology) or hedonic tone, the (emotional) value associated with an event, object or situation Places France * Valence, Charente, a commune in the Charente department * Valence, Drôme, Drôme, a commune and prefecture of the Drôme department ** University of Valence, a medieval university * Valence, Tarn-et-Garonne, a commune in the Tarn-et-Garonne department * Canton of Valence, Tarn-et-Garonne department * Arrondissement of Valence, Drôme department * Roman Catholic Diocese of Valence * Valence-d'Albigeois, in the Tarn department * Valence-en-Brie, in the Seine-et-Marne department * Valence-sur-Baïse, in the Gers department * Bourg-lès-Valence, in the Drôme department England * Riv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
