Past exam of the advanced quantum physics course of the University of Cambridge / 2014 / Paper 1 / 3 / a / Solution

At zero field, the spin-one-half triplet state has energy $\Delta /4$ and degeneracy three; the spin-one-half singlet state has energy $-3\Delta /4$ and degeneracy one:For $\Delta >0$ the singlet is lower; for $\Delta <0$ the triplet is lower. If $\Delta =0$, all four states coincide.