Abstract
It is proven that all Abelian monopoles of SU(N) are unstable while SU(N)/Z(N) always has 2/sup N/-2 species of stable monopoles. It is argued that the presence (absence) of a phase transition in SU(N)/Z(N) (SU(N)) lattice gauge theories for N = 2 and 3 follows solely from the qualitative distinction between stable and unstable, and hence is a lattice artifact irrelevant to the continuum limit. The SU(Ngreater than or equal to4) transitions are briefly discussed.
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