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Analogs of merons and meron pairs in the XY model

Daniel R. Stump

  • Physics Department, Indiana University, Bloomington, Indiana 47405

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Phys. Rev. D 20, 2592 – Published 15 November, 1979

DOI: https://doi.org/10.1103/PhysRevD.20.2592

Abstract

A path-integral formula for the vacuum wave functional is used to show that merons in quantum chromodynamics produce long-range vacuum fluctuations of the form of Wu-Yang monopoles, whereas meron pairs or instantons produce only short-range fluctuations. The existence of long-range vacuum fluctuations may be related to the problem of quark confinement. The XY model, which describes classical two-component spins on a two-dimensional lattice, is reviewed. Vortex spin-field configurations, which are responsible for the existence of a disordered phase in the XY model, are shown to be analogous to merons in that they produce long-range fluctuations of the spins along a given axis. The analogy is emphasized by considering the analog of the vacuum wave functional in the XY model. It is argued that the vortex-antivortex pairs that occur in the ordered phase of the XY model are analogous to meron pairs or instantons in quantum chromodynamics.

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Phys. Rev. D 20, 2592– Published 15 November, 1979
  • Received 21 May 1979

© 1979 American Physical Society

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