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Home > Art, Film & Photography > Quantum Magnetism: Heisenberg Model, Majumdar-Ghosh Model, Magnetic Translation, J1 J2 Model, Quantum Spin Model
Quantum Magnetism: Heisenberg Model, Majumdar-Ghosh Model, Magnetic Translation, J1 J2 Model, Quantum Spin Model

Quantum Magnetism: Heisenberg Model, Majumdar-Ghosh Model, Magnetic Translation, J1 J2 Model, Quantum Spin Model


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About the Book

Chapters: Heisenberg Model, Majumdar-ghosh Model, Magnetic Translation, J1 J2 Model, Quantum Spin Model. Source: Wikipedia. Pages: 22. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: The Heisenberg model is a statistical mechanical model used in the study of critical points and phase transitions of magnetic systems, in which the spin of the magnetic systems are treated quantum mechanically. In the prototypical Ising model, defined on a d-dimensional lattice, at each lattice site, a spin represents a microscopic magnetic dipole to which the magnetic moment is either up or down. For quantum mechanical reasons (see exchange interaction or the subchapter "quantum-mechanical origin of magnetism" in the article on magnetism), 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) the Hamiltonian can be written in the form for a 1-dimensional model consisting of N dipoles, represented by classical vectors (or "spins") j, subject to the periodic boundary condition . The Heisenberg model is a more realistic model in that it treats the spins quantum-mechanically, by replacing the spin by a quantum operator (Pauli spin-1/2 matrices at spin 1/2), and the coupling constants and . As such in 3-dimensions, the Hamiltonian is given by where the on the right-hand side indicates the external magnetic field, with periodic boundary conditions, and at spin, spin matrices given by The Hamiltonian then acts upon the tensor product, of dimension . The objective is to determine the spectrum of the Hamiltonian, from which the partition function can be calculated, from which the thermodynamics of the system can be studied. The most widely known type of Heisenberg mo...More: http: //booksllc.net/?id=4899779


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Product Details
  • ISBN-13: 9781158627950
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Heisenberg Model, Majumdar-Ghosh Model, Magnetic Translation, J1 J2 Model, Quantum Spin Model
  • Width: 229 mm
  • ISBN-10: 1158627955
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Spine Width: 1 mm
  • Weight: 50 gr


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