Analogs of merons and meron pairs in theXYmodel

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 $\mathrm{XY}$ 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 $\mathrm{XY}$ 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 $\mathrm{XY}$ model. It is argued that the vortex-antivortex pairs that occur in the ordered phase of the $\mathrm{XY}$ model are analogous to meron pairs or instantons in quantum chromodynamics.