In conventional particle physics settings, the field is generally taken to be SU(N), or the vector subspace of quotient ( S U ( N ) L × × S U ( N ) R ) / S U ( N ) of the product of left and right chiral fields. In condensed matter theories, the field is taken to be O(N). For the rotation group O(3), the sigma model describes the isotropic ferromagnet ; more generally, the O(N) model shows up in the quantum Hall effect, superfluid Helium-3 and spin chains.