Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in or
create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision |
Your text |
Line 1: |
Line 1: |
| {{Stub-general}}
| | [[Category: Models]] |
| The '''Heisenberg model''' is the n=3 case of the ''n''-vector model. The [[Hamiltonian]] is given by
| |
| | |
| :<math>H = -J{\sum}_{\langle i,j\rangle}\mathbf{S}_i \cdot \mathbf{S}_{j}</math> | |
| | |
| where the sum runs over all pairs of nearest neighbour spins, <math>\mathbf{S}</math>, and where <math>J</math> is the coupling constant.
| |
| The classical model is known to have a finite-temperature phase transition in three or higher spacial dimensions, and the ferromagnetic (<math>J>0</math>) and antiferromagnetic (<math>J<0</math>) share essentially the same physics.
| |
| The quantum version differs greatly, and even the one-dimensional case has a rich variety of phenomena depending on the spin number <math>S</math> and the sign of <math>J</math>.
| |
| | |
| ==See also==
| |
| *[[Ising Models]] (n=1)
| |
| *[[XY model]] (n=2)
| |
| *[[Mermin-Wagner theorem]]
| |
| ==References==
| |
| #[http://dx.doi.org/10.1016/0031-8914(64)90223-X A. C. Hewson and D. Ter Haar "On the theory of the Heisenberg ferromagnet", Physica '''30''' pp. 271-276 (1964)]
| |
| #[http://dx.doi.org/10.1063/1.335131 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)]
| |
| #[http://dx.doi.org/10.1103/PhysRevLett.80.3535 F. Lado and E. Lomba "Heisenberg Spin Fluid in an External Magnetic Field ", Physical Review Letters '''80''' pp. 3535-3538 (1998)]
| |
| #[http://dx.doi.org/10.1140/epjb/e2003-00246-8 E. Lomba, C. Martín and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B '''34''' pp. 473-478 (2003)]
| |
| [[Category: Magnetism]] | | [[Category: Magnetism]] |
| [[Category: Models]]
| |