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We analyse a $2+1$ dimensional model with charged, relativistic fermionsinteracting through a four-Fermi term. Taking advantage of its large-$N$renormalizability, the various phases of this model are studied at finitetemperature and beyond the leading order in $1/N$. Although the vacuumexpectation value (VEV) of a charged order parameter is zero at any non-zerotemperature, the model nevertheless exhibits a rich phase structure in thestrong coupling r\'egime, because of the non-vanishing VEV of a neutral orderparameter and due to the non-trivial dynamics of the vortex excitations on theplane. These are: a confined-vortex phase which is superconducting at lowtemperatures, an intermediate-temperature phase with deconfined vortices, and ahigh-temperature phase, where the neutral order parameter vanishes. Themanifestation of superconductivity at low-temperatures and its disappearanceabove a critical temperature is explicitly shown to be due to the vortexconfinement/deconfinement mechanism of Kosterlitz and Thouless. The groundstate does not break parity or time-reversal symmetries and the ratio of theenergy gap to $T_c$ is bigger than the conventional BCS value, for $N\ltwid22$.Comment: 27 pages + 4 figures and several diagrammatic equations, available  from authors upon request, UdeM-LPN-TH-14

SUPERCONDUCTIVITY IN 2+1 DIMENSIONS VIA KOSTERLITZ-THOULESS MECHANISM: LARGE N AND FINITE TEMPERATURE ANALYSES