Exchange frequencies in two-dimensional solids

B. Bernu, D. M. Ceperley

Research output: Contribution to journalArticlepeer-review


In quantum solids composed of fermion particles, such as helium-3 and electrons, the low-temperature physics is governed by spin exchanges, according to the Thouless theory. We present path integral Monte Carlo calculations of ring exchange energies on 'clean' two-dimensional crystals of both helium-3 and electrons. We see a remarkable similarity of the results for these two 'opposite' systems. They are both ferromagnetic in the semi-classical limit (strong coupling) and antiferromagnetic near the melting transition where the relative exchange energies become equivalent. We focus here on the importance of long-ring exchanges near the melting transition. The total energy associated to exchanges may diverge, leading to a possible mechanism for the melting transition.

Original languageEnglish (US)
Pages (from-to)9099-9107
Number of pages9
JournalJournal of Physics Condensed Matter
Issue number40 SPEC.
StatePublished - Oct 14 2002

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics


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