ϕ4 lattice model with cubic symmetry in three dimensions: Renormalization group flow and first-order phase transitions

We study the three-component φ⁴ model on the simple cubic lattice in the presence of a cubic perturbation. To this end, we perform Monte Carlo simulations in conjunction with a finite-size scaling analysis of the data. The analysis of the renormalization group (RG) flow of a dimensionless quantity provides us with the accurate estimate Y₄-ω₂=0.0000.16em0ex81(7) for the difference of the RG eigenvalue Y₄ at the O(3)-symmetric fixed point and the correction exponent ω₂ at the cubic fixed point. We determine an effective exponent νeff of the correlation length that depends on the strength of the breaking of the O(3) symmetry. Field theory predicts that depending on the sign of the cubic perturbation, the RG flow is attracted by the cubic fixed point, or runs to an ever increasing amplitude, indicating a fluctuation-induced first-order phase transition. We demonstrate directly the first-order nature of the phase transition for a sufficiently strong breaking of the O(3) symmetry. We obtain accurate results for the latent heat, the correlation length in the disordered phase at the transition temperature, and the interface tension for interfaces between one of the ordered phases and the disordered phase. We study how these quantities scale with the RG flow, allowing quantitative predictions for weaker breaking of the O(3) symmetry.