If the exchange interaction constant J < 0 , then for low temperature nearest spins are anti-aligned. In the simplest Ising antiferromagnetic on square grid they form two ordered sub-lattices (disposed as cells on a chess-board). Starting at random configuration you can see clusters of ordered phase formation and movement of domain walls. The Metropolis algorithm is used in the applet bellow. |
It is funny that antiferromagnetic ordering appears in the thermostat
algorithm for negative temperature (see below).
But in contrast to ferromagnetic two vectors L and -L correspond to the same physical state of antiferromagnetic. Therefore opposite poins on the sphere L^{2} = 1 are equivalent. The closed contour 1 on the picture to the left may be shrunk into a point. The contour 2 is closed as since it goes through opposite (equivalent) points. The second contour is not equivalent to the first one, therefore in antiferromagnetics there are topological solitons - disclinations. |
+ - + - o - + - + - o + - + o o | On a square lattice antiferromagnetic ordering is evident. But you see that on a triangular lattice it is impossible to place + and - so that neighboring nodes always have opposite orientations (this phenomenon is called- frustration). |