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 $S_{i}=\pm 1$ and the summation runs over the lattice sites.

The order parameter is $m=\sum _{i}S_{i}$

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