= Classical Heisenberg model
{title2=$E=-J\sum_{\langle ij\rangle}\mathbf s_i\cdot\mathbf s_j,\quad|\mathbf s_i|=1$}
The <classical Heisenberg model> assigns a three-component unit <vector> to each site and couples pairs by their <dot product>. Positive $J$ 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.<Statistical Field Theory by David Tong>[§4.2, $O(3)$ Heisenberg model]{ref}
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