title: Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice.
abstract: We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.
authors.affiliation: Instituto de Física, Universidade de São Paulo, São Paulo, Brazil.
authors.forename: E
authors.initials: E
authors.lastname: do Carmo
authors.forename: A P
authors.initials: AP
authors.lastname: Vieira
authors.forename: S R
authors.initials: SR
authors.lastname: Salinas