Giovanni De Matteis

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.

We further pursue the analysis of a mean-field model recently proposed by Sonnet et al. [Phys. Rev. E 67, 061701 (2003)] to describe nematic biaxial phases. This model, which is based on a simplified version of Straley’s pair potential, is characterized by the prediction of a tricritical point along the transition line between uniaxial and biaxial phases. We show that the same model predicts another tricritical point, but along the line of the direct isotropic-to-biaxial transition. Our prediction is quantitative, as it stems from an analytical criterion for tricriticality.