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 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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)

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

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 }

See also

• Critical exponents