Counterexamples to ferromagnetic ordering of energy levels
Journal of Mathematical Physics
The Heisenberg ferromagnet has symmetry group SU(2). The property known as ferromagnetic ordering of energy levels (FOEL) states that the minimum energy eigenvalue among eigenvectors with total spin s is monotone decreasing as a function of s. While this property holds for certain graphs such as open chains, in this note we demonstrate some counterexamples. We consider the spin 1/2 model on rings of length 2n for n=2,3,...,8, and show that the minimum energy among all spin singlets is less than
... or equal to the minimum energy among all spin triplets, which violates FOEL. This also shows some counterexamples to the "Aldous ordering" for the symmetric exclusion process. We also review some of the literature related to these examples.