EXERCISE S10.10. A spin system has Hamiltonian = -ara-1), where a and denote lattice sites, the coupling constant, J(rare), depends only on the magnitude of the dis- placement, ra- rs, between sites a and B, and S. and Sa are the spin operators associated with sites a and B. The total spin, Stor = a Sa commutes with the Hamiltonian so [, Stor] = 0. Show that if (Sz,tot) = Mo and (Stor)=(y,tot) = 0, the rotational symmetry of the system about the z axis is preserved but about the x and y axes it is broken (rotational symmetry about axis i is preserved if [peq, Si,tor] = 0).