Ising model: Difference between revisions
Carl McBride (talk | contribs) |
Carl McBride (talk | contribs) m (→Ising Model) |
||
| Line 10: | Line 10: | ||
between nearest neighbors. | between nearest neighbors. | ||
<math> \frac{U}{k_B T} = - K \sum_{ | <math> \frac{U}{k_B T} = - K \sum_{\langle ij \rangle} S_i S_j </math> | ||
where <math> | where <math> \langle ij \rangle </math> indicates that the sum is done over nearest neighbors, and | ||
<math> S_i </math> indicates the state of the i-th site. | <math> S_i </math> indicates the state of the i-th site. | ||
Revision as of 11:25, 23 February 2007
Ising Model
The Ising model is commonly defined over an ordered lattice. Each site of the lattice can adopt two states: either UP (S=+1) or DOWN (S=-1).
The energy of the system is the sum of pair interactions between nearest neighbors.
where indicates that the sum is done over nearest neighbors, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S_i } indicates the state of the i-th site.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K } is called the Coupling constant.
to be continued:
Ising Model (1 dimensional)
- Ising in 1-dimension (exact solution)
Other topics
- Usual lattices in 2d: Critical behavior
- Lattices in 3-d
- Ferromagnetic and antiferromagnetic couplings
- Frustration, etc
- Simulation procedures
- Theoretical methods