Universality classes

$d$	$n$	$\sigma$	name
			3-state Potts
			Ashkin-Teller
			Chiral
			Directed percolation
			Ising
			Local linear interface
			Mean-field
			Molecular beam epitaxy
			Random-field

Ising

The Hamiltonian of the Ising model is

$H={\sum }_{<i,j>}{S}_i{S}_j$

where $S_i=\pm 1<math>andthesummationrunsoverthelatticesites.Theorderparameteris<math>m={\sum }_i{S}_i$

In two dimensions, Onsager obtained the exact solution in the absence of a external field, and the critical exponents are $\alpha =0$ (In fact, the specific hear diverges logarithmically with the critical temperature)

$\beta =\frac{1}{8}$

$\gamma =\frac{7}{4}$

$\delta =15$

See also

• Critical exponents