Ising model: Difference between revisions

Revision as of 11:25, 23 February 2007

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.

${\frac {U}{k_{B}T}}=-K\sum _{\langle ij\rangle }S_{i}S_{j}$

where $\langle ij\rangle$ indicates that the sum is done over nearest neighbors, and $S_{i}$ indicates the state of the i-th site.

$K$ is called the Coupling constant.

to be continued:

@@ Line 10: / Line 10: @@
 between nearest neighbors.
-<math> \frac{U}{k_B T} = - K \sum_{<ij>} S_i S_j </math>
+<math> \frac{U}{k_B T} = - K \sum_{\langle ij \rangle} S_i S_j </math>
-where <math> <ij> </math> indicates that the sum is done over nearest neighbors, and
+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.