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.
Keywords
Cite
@article{arxiv.1009.2729,
title = {Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice},
author = {E. do Carmo and A. P. Vieira and S. R. Salinas},
journal= {arXiv preprint arXiv:1009.2729},
year = {2015}
}