The mass dependence of the chiral phase transition is studied in the linear
$SU(3)\times SU(3)$ sigma-model to leading order in a $1/N_f$-expansion, $N_f$
denoting the number of flavours. For realistic meson masses we find a smooth
crossover between $T\sim181.5$ to 192.6~[MeV]. The crossover looks more rapid
in the light quark condensate than in thermodynamic quantities like the energy
and entropy densities. The change in the light quark condensate in this
temperature interval is $\sim$~50\% of the zero-temperature condensate value,
while the entropy density increases by ($5.5\pm0.8)\cdot10^{-3}$~[GeV$^3$].
Since the numerical error is particularly large in this region, we cannot rule
out a finite latent heat smaller than 0.2~[GeV/fm$^3$]. The chiral transition
is washed out for an average pseudoscalar meson octet mass of 203~[MeV]. This
gives an upper bound on the first-order transition region in the meson mass
parameter space. The corresponding ratio of critical to realistic light current
quark masses $m^{crit}_{u,d}/m_{u,d}$ is estimated as $0.26\pm0.08$. This
result is by an order of magnitude larger than the corresponding mean-field
value. Therefore theComment: LaTeX, HD--TVP--94--16, Please contact authors via email for figure