"I feel dizzy, Doctor".

Diagnosing the underlying cause of this common complaint can be challenging because many conditions present with dizziness. This review--and accompanying algorithm--can guide your evaluation.

Ferromagnetic Lieb-Mattis theorem.

We prove ferromagnetic ordering of energy levels for XXX Heisenberg chains with spins of arbitrary magnitude, thus extending our previous result for the spin-1/2 chain. Ferromagnetic ordering means that the minimum energies in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin. This result provides a ferromagnetic analogue of the well-known theorem by Lieb and Mattis about ordering of energy levels in antiferromagnetic and ferrimagnetic systems on bipartite graphs.