  We study a $U(N)\times U(N)$ symmetric scalar field model in four and three
dimensions. First, using our data in four dimensions in the weak coupling
region, we demonstrate explicitly that the observed first order phase
transition is induced by quantum fluctuations. Next, based on the
renormalization group and our new simulation results in three dimensions we
argue that even if the $U_A(1)$ symmetry is restored below the critical
temperature the QCD finite temperature chiral phase transition for two flavor
could be extremely weak first order. Contribution to Lattice '93 proceedings.
Needs espcrc2.sty file (included). Search Figure1.ps, Figure2.ps, ... for
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