  In order to deepen our understanding of the nature of the deconfinement phase
transition for various gauge groups, we investigate SU(4) Yang-Mills theory in
2+1 dimensions. We find that the transition is weakly first order. We perform
extensive Monte Carlo simulations on lattices with temporal extent N_t = 3, 4
and 5, and spatial sizes up to N_s = 20 N_t. We observe coexistence of confined
and deconfined phases at the critical temperature, and finite-size scaling
shows consistency with first order exponents. The continuum extrapolation of
the latent heat yields L_h/T_c^3=0.188(17).
