Universality classes: Difference between revisions
Jump to navigation
Jump to search
(→Ising) |
(→Ising) |
||
| Line 28: | Line 28: | ||
==Ising== | ==Ising== | ||
The Hamiltonian of the Ising model is | The Hamiltonian of the Ising model is | ||
\begin{equation} | \begin{equation} | ||
{\cal H}=\sum{<i,j>}S_iS_j | {\cal H}=\sum{<i,j>}S_iS_j | ||
\end{equation} | \end{equation} | ||
where $S_i=\pm 1$ and the summation runs over the lattice sites. | where $S_i=\pm 1$ and the summation runs over the lattice sites. | ||
The order parameter is | The order parameter is | ||
\begin{equation} | \begin{equation} | ||
| Line 42: | Line 45: | ||
\end{equation} | \end{equation} | ||
(In fact, the specific hear diverges logarithmically with the critical temperature) | (In fact, the specific hear diverges logarithmically with the critical temperature) | ||
\begin{equation} | \begin{equation} | ||
\beta=\frac{1}{8} | \beta=\frac{1}{8} | ||
Revision as of 14:01, 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
\begin{equation} {\cal H}=\sum{<i,j>}S_iS_j \end{equation}
where $S_i=\pm 1$ and the summation runs over the lattice sites.
The order parameter is \begin{equation} m=\sum_i S_i \end{equation}
In two dimensions, Onsager obtained the exact solution in the absence of a external field, and the critical exponents are \begin{equation} \alpha=0 \end{equation} (In fact, the specific hear diverges logarithmically with the critical temperature)
\begin{equation} \beta=\frac{1}{8} \end{equation} \begin{equation} \gamma=\frac{7}{4} \end{equation} \begin{equation} \delta=15 \end{equation}