Abstract
Diamagnetic and critical properties of non-Abelian and Abelian lattice Higgs models are discussed: matter fields always behave diamagnetically under couplings to gauge fields. For some Abelian models, the photon-photon interactions is found to be attractive, a Higgs mechanism is exhibited, and in two dimensions fractionally charged quarks are permanently confined. In three dimensions there is a Higgs-QED phase transition, with confinement in the QED phase. It is argued that a similar transition occurs in four dimensions, with liberated magnetic monopoles in the QED phase, but electric monopoles, “quarks”, are never confined. Conjectures concerning confinement in non-Abelian models are described.
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