We extend the analysis of a mean-field model for biaxial liquid crystals recently proposed by Sonnet et al. Phys. Rev. E 67 061701 (2003)]. In particular, we perform a bifurcation analysis of the equilibrium equations and derive the complete phase diagram. We show that two order parameters suffice to label all equilibrium phases, though they exhibit different bifurcation patterns. A Monte Carlo simulation study is performed as well, confirming qualitatively the predictions of this analysis.
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