Universality classes: Difference between revisions
Jump to navigation
Jump to search
(→Ising) |
(→Ising) |
||
| Line 30: | Line 30: | ||
<math> | <math> | ||
H=\ | H=\sum_{<i,j>}S_i S_j | ||
</math> | </math> | ||
where | where <math>S_i=\pm 1<math> and the summation runs over the lattice sites. | ||
The order parameter is | The order parameter is | ||
<math> | |||
m=\sum_i S_i | m=\sum_i S_i | ||
</math> | |||
In two dimensions, Onsager obtained the exact solution in the absence of a external field, and the critical exponents are | In two dimensions, Onsager obtained the exact solution in the absence of a external field, and the critical exponents are | ||
<math> | |||
\alpha=0 | \alpha=0 | ||
</math> | |||
(In fact, the specific hear diverges logarithmically with the critical temperature) | (In fact, the specific hear diverges logarithmically with the critical temperature) | ||
<math> | |||
\beta=\frac{1}{8} | \beta=\frac{1}{8} | ||
</math> | |||
<math> | |||
\gamma=\frac{7}{4} | \gamma=\frac{7}{4} | ||
</math> | |||
<math> | |||
\delta=15 | \delta=15 | ||
</math> | |||
==Local linear interface== | ==Local linear interface== | ||
Revision as of 13:11, 20 July 2011
|
This article is a 'stub' page, it has no, or next to no, content. It is here at the moment to help form part of the structure of SklogWiki. If you add sufficient material to this article then please remove the {{Stub-general}} template from this page. |
| name | |||
| 3-state Potts | |||
| Ashkin-Teller | |||
| Chiral | |||
| Directed percolation | |||
| Ising | |||
| Local linear interface | |||
| Mean-field | |||
| Molecular beam epitaxy | |||
| Random-field |
3-state Potts
Ashkin-Teller
Chiral
Directed percolation
Ising
The Hamiltonian of the Ising model is
where
In two dimensions, Onsager obtained the exact solution in the absence of a external field, and the critical exponents are (In fact, the specific hear diverges logarithmically with the critical temperature)
