Absence of ordering in certain isotropic systems

M. F. Thorpe

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Abstract

The method of Mermin and Wagner [Phys. Rev. Lett. 17, 1133 (1966)] is used to show that one- and two-dimensional spin systems interacting with a general isotropic interaction H=1/2 Σ ijnij (n) (Si·Sj)n, where the exchange interactionsIij(n) are of finite range, cannot order in the sense that 〈Oi〉=0 for all traceless operators Oi defined at a single site i. Mermin and Wagner have proved the above for the case n = 1 with Oi = Si, i.e., for the Heisenberg Hamiltonian. The proof allows us to rule out the possibility that a small isotropic biquadratic exchange (Si·Sj) 2 could induce ferromagnetism or antiferromagnetism in a two-dimensional Heisenberg system.

Original languageEnglish (US)
Pages (from-to)1410-1411
Number of pages2
JournalJournal of Applied Physics
Volume42
Issue number4
DOIs
StatePublished - Dec 1 1971

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

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