SO(3) vortices as a mechanism for generating a mass gap in the 2D SU(2) principal chiral model

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Abstract

We propose a mechanism that can create a mass gap in the SU(2) chiral spin model at arbitrarily small temperatures. We give a sufficient condition for the mass gap to be non-zero in terms of the behaviour of an external ℤ(2) flux introduced by twisted boundary conditions. This condition in turn is rewritten in terms of an effective dual Ising model with an external magnetic field generated by SO(3) vortices. We show that having a non-zero magnetic field in the effective Ising model is sufficient for the SU(2) system to have a mass gap. We also show that certain vortex correlation inequalities, if satisfied, would imply a non-zero effective magnetic field. Finally, we give some plausibility arguments and Monte Carlo evidence for the required correlation inequalities.

Original languageEnglish
Pages (from-to)613-638
Number of pages26
JournalNuclear Physics B
Volume482
Issue number3
DOIs
Publication statusPublished - Dec 30 1996

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vortices
Ising model
magnetic fields
boundary conditions
temperature

Keywords

  • Confinement
  • Disorder
  • Lattice
  • SU(2) principal chiral model

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

SO(3) vortices as a mechanism for generating a mass gap in the 2D SU(2) principal chiral model. / Kovács, T.

In: Nuclear Physics B, Vol. 482, No. 3, 30.12.1996, p. 613-638.

Research output: Contribution to journalArticle

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