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We study the thermodynamics of large N pure 2+1 dimensional Yang-Mills theoryon a small spatial sphere. By studying the effective action for the Polyakovloop order parameter, we show analytically that the theory has a second orderdeconfinement transition to a phase where the eigenvalue distribution of thePolyakov loop is non-uniform but still spread over the whole unit circle. At ahigher temperature, the eigenvalue distribution develops a gap, via anadditional third-order phase transition. We discuss possible forms of the fullphase diagram as a function of temperature and sphere radius. Our resultstogether with extrapolation of lattice results relevant to the large volumelimit imply the existence of a critical radius in the phase diagram at whichthe deconfinement transition switches from second order to first order. We showthat the point at the critical radius and temperature can be either atricritical point with universal behavior or a triple point separating threedistinct phases.Comment: 34 pages, LaTeX, 6 figures, typos correcte

A second order deconfinement transition for largeN2+1 dimensional Yang-Mills theory on a smallS2

A second order deconfinement transition for largeN2+1 dimensional Yang-Mills theory on a smallS²