The classical limit of quantum spin systems

Elliott Lieb

Research output: Contribution to journalArticle

308 Scopus citations

Abstract

We derive a classical integral representation for the partition function, ZQ, of a quantum spin system. With it we can obtain upper and lower bounds to the quantum free energy (or ground state energy) in terms of two classical free energies (or ground state energies). These bounds permit us to prove that when the spin angular momentum J → ∞ (but after the thermodynamic limit) the quantum free energy (or ground state energy) is equal to the classical value. In normal cases, our inequality is ZC(J)≦ZQ(J)≦ZC(J+1).

Original languageEnglish (US)
Pages (from-to)327-340
Number of pages14
JournalCommunications in Mathematical Physics
Volume31
Issue number4
DOIs
StatePublished - Dec 1 1973

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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