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Classical Heisenberg model : ウィキペディア英語版
Classical Heisenberg model
The Classical Heisenberg model is the n = 3 case of the n-vector model, one of the models used in statistical physics to model ferromagnetism, and other phenomena.
==Definition==
It can be formulated as follows: take a d-dimensional lattice, and a set of spins of the unit length
:\vec_i \in \mathbb^3, |\vec_i|=1\quad (1),
each one placed on a lattice node.
The model is defined through the following Hamiltonian:
: \mathcal = -\sum_ \mathcal_ \vec_i \cdot \vec_j\quad (2)
with
: \mathcal_ = \begin J & \mboxi, j\mbox \\ 0 & \mbox\end
a coupling between spins.

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