The isotropy of the model is actually not important to the fact that it has an exactly dimerised ground state. For example, H ^ ^ = J ∑ ∑ j = 1 N ( X j X j + 1 + Y j Y j + 1 + δ δ Z j Z j + 1 ) + J 2 ∑ ∑ j = 1 N ( X j X j + 2 + Y j Y j + 2 + δ δ Z j Z j + 2 ) also has the same aforementioned exactly dimerised ground state for all real δ δ > − − 1 / 2 .