Heisenberg model
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The Heisenberg model is the n=3 case of the n-vector model. The Hamiltonian is given by
\[H = -J{\sum}_{\langle i,j\rangle}\mathbf{S}_i \cdot \mathbf{S}_{j}\]
where the sum runs over all pairs of nearest neighbour spins, \(\mathbf{S}\), and where \(J\) is the coupling constant.
[edit] See also
- Ising Models (n=1)
- XY model (n=2)
- Mermin-Wagner theorem
[edit] References
- A. C. Hewson and D. Ter Haar "On the theory of the Heisenberg ferromagnet", Physica 30 pp. 271-276 (1964)
- T. M. Giebultowicz and J. K. Furdyna "Monte Carlo simulation of fcc Heisenberg antiferromagnet with nearest- and next-nearest-neighbor interactions", Journal of Applied Physics 57 pp. 3312-3314 (1985)
- F. Lado and E. Lomba "Heisenberg Spin Fluid in an External Magnetic Field ", Physical Review Letters 80 pp. 3535-3538 (1998)
- E. Lomba, C. MartÃn and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B 34 pp. 473-478 (2003)
