We study the large N limit in the presence of magnetic monopoles in the
Yang-Mills/Higgs model in three dimensions. The physics in the limit depends
strongly on the distribution of eigenvalues of the Higgs field in the vacuum,
and we propose a particular, nondegenerate configuration. It minimizes the free
energy at the moment of symmetry breaking. Given this, the magnetic monopoles
show a wide hierarchy of masses, and some are vanishing as 1/N. The dilute gas
picture, then, provides an interesting structure in the large N limit.Comment: 36 pages, 5 figures, changes in style, organization and small errors
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