The Classical Heisenberg model is a theoretical framework used to describe the magnetic properties of a system of spins (or magnetic moments) arranged on a lattice. It is based on the concepts of classical mechanics and statistical mechanics, and it provides insights into phenomena such as ferromagnetism and antiferromagnetism.
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The classical Heisenberg model assigns a three-component unit vector to each site and couples pairs by their dot product. Positive favors parallel alignment. With no applied magnetic field or anisotropy, simultaneous rotations of all vectors preserve the energy, so an ordered state chooses a direction and exhibits spontaneous symmetry breaking. The vector order parameter is the spatially averaged orientation. A quartic Landau free energy describes its mean-field onset near a continuous transition; fluctuations can change the critical exponents.[ref]