Editing Heisenberg model
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where the sum runs over all pairs of nearest neighbour spins, <math>\mathbf{S}</math>, and where <math>J</math> is the coupling constant. | where the sum runs over all pairs of nearest neighbour spins, <math>\mathbf{S}</math>, and where <math>J</math> is the coupling constant. | ||
The classical model is known to have a | The classical model is known to have a phase transition in three or higher spacial dimensions, and the ferromagnetic (<math>J>0</math>) and antiferromagnetic (<math>J<0</math>) share essentially the same physics. | ||
The quantum version differs greatly, and even the one-dimensional case has a rich variety of phenomena depending on the spin number <math>S</math> and the sign of <math>J</math>. | The quantum version differs greatly, and even the one-dimensional case has a rich variety of phenomena depending on the spin number <math>S</math> and the sign of <math>J</math>. | ||