Universality classes: Difference between revisions
(→Ising) |
Carl McBride (talk | contribs) m (→Ising: Added some internal links) |
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==Directed percolation== | ==Directed percolation== | ||
==Ising== | ==Ising== | ||
The Hamiltonian of the Ising model is | The [[Hamiltonian]] of the [[Ising model]] is | ||
<math> | <math> | ||
| Line 36: | Line 36: | ||
where <math>S_i=\pm 1</math> and the summation runs over the lattice sites. | where <math>S_i=\pm 1</math> and the summation runs over the lattice sites. | ||
The order parameter is | The [[Order parameters | order parameter]] is | ||
<math> | <math> | ||
m=\sum_i S_i | m=\sum_i S_i | ||
</math> | </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> | <math> | ||
\alpha=0 | \alpha=0 | ||
</math> | </math> | ||
(In fact, the specific | (In fact, the [[Heat capacity |specific heat]] diverges logarithmically with the [[Critical points |critical temperature]]) | ||
<math> | <math> | ||
Revision as of 14:46, 20 July 2011
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| 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 and the summation runs over the lattice sites.
The order parameter is
In two dimensions, Onsager obtained the exact solution in the absence of a external field, and the critical exponents are 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 \alpha=0 } (In fact, the specific heat diverges logarithmically with the critical temperature)
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 \beta=\frac{1}{8} }
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 \gamma=\frac{7}{4} }
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 \delta=15 }