Most magnets are crystals, which already have broken the rotational symmetry. For some ``Heisenberg'' magnets, the effects of the crystal on the magnetism is small. Magnets are really distinguished by the fact that they break time-reversal symmetry: if you reverse the arrow of time, the magnetization would change direction!

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Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).