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

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We numerically investigate the three-dimensional O(6) model on 12³ to 120³ 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 Jc=1.42865(3). The universal value of the Binder cumulant at this point is gᵣ(Jc)=-1.94456(10). At the critical coupling, the critical exponents γ=1.604(6), β=0.425(2) and ν=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.