Ordering Energy Levels of Interacting Spin Systems

Elliott Lieb and Daniel Mattis
Additional contact information
Elliott Lieb: International Business Machines Corporation, Thomas J. Watson Research Center
Daniel Mattis: International Business Machines Corporation, Thomas J. Watson Research Center

A chapter in Inequalities, 2002, pp 43-45 from Springer

Abstract: Abstract The total spin S is a good quantum number in problems of interacting spins. We have shown that for rather general antiferromagnetic or ferrimagnetie Hamiltonians, which need not exhibit translational invariance, the lowest energy eigenvalue for each value of S [denoted E(S) ] is ordered in a natural way. In antiferromagnetism, E(S + 1) > E(S) for S ≥ 0. In ferrimagnetism, E(S + 1) > E(S) for S ≥ S, and in addition the ground state belongs to S ≤ S. S is defined as follows: Let the maximum spin of the A sublattice be S A and of the B sublattice S B; then S = S A—S B. Antiferromagnetism is treated as the special case of S = 0. We also briefly discuss the structure of the lowest eigenfunctions in an external magnetic field.

Date: 2002
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55925-9_3

Ordering information: This item can be ordered from
http://www.springer.com/9783642559259

DOI: 10.1007/978-3-642-55925-9_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().