A Ferromagnetic Lieb-Mattis Theorem
Mathematical Physics
2007-05-23 v3 Statistical Mechanics
math.MP
Abstract
We prove ferromagnetic ordering of energy levels for XXX Heisenberg chains of any spin and XXZ spin chains with all spins equal to 1/2. 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.
Keywords
Cite
@article{arxiv.math-ph/0408020,
title = {A Ferromagnetic Lieb-Mattis Theorem},
author = {Bruno Nachtergaele and Shannon Starr},
journal= {arXiv preprint arXiv:math-ph/0408020},
year = {2007}
}
Comments
4 pages, final version, some references added