Critical behavior and scaling functions of the three-dimensional O(6) model

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 behavior of the magnetization on the pseudocritical line.