Bifurcation Analysis of Liquid Crystal Phase Transitions

Abstract

These lectures focus on bifurcation analysis as a tool for studying phase transitions that occur in models of liquid-crystalline systems. We show how this approach bridges the gap between the phenomenological Landau theory and the --- often intractable --- full statistical mechanical treatment. Employing a `toy model' as a tutorial example the various ingredients of the technique are presented. Special attention is paid to the way in which one obtains information on the relation between the characteristics of the assumed interparticle interactions (shape, symmetry ...) and global properties of the phase transitions (order, symmetry of resultant phases ...). Finally, a few more involved examples are discussed indicating how the approach can be applied to more realistic models and how it can serve as a complement to simulations.