  We numerically investigate the three-dimensional O(6) model on 12^3 to 120^3
lattices within the critical region at zero magnetic field, as well as at
finite magnetic field on the critical isotherm and for several fixed couplings
in the broken and the symmetric phase. We obtain from the Binder cumulant at
vanishing magnetic field the critical coupling J_c=1.42865(3). The universal
value of the Binder cumulant at this point is g_r(J_c)=-1.94456(10). At the
critical coupling, the critical exponents \gamma=1.604(6), \beta=0.425(2) and
\nu=0.818(5) are determined from a finite-size-scaling analysis. Furthermore,
we verify predicted effects induced by massless Goldstone modes in the broken
phase. The results are well described by the perturbative form of the model's
equation of state. Our O(6)-result is compared to the corresponding Ising, O(2)
and O(4) scaling functions. Finally, we study the finite-size-scaling behaviour
of the magnetisation on the pseudocritical line.
