A Magnetic Model with a Possible Chern-Simons Phase

The effect of perturbation is studied algebraically: the ground state space G◦, of H◦, is described as a surface algebra and our ansatz is that perturbation should respect this structure yielding a perturbed ground state G, described by a quotient algebra. By classification, this implies G, ∼= DE. The fundamental point is that nonlinear structures may be present on degenerate eigenspaces of an initial H◦ which constrain the possible effective action of a perturbation.