Liquid Crystals in Two Dimensions: First-Order Phase Transitions and Nonuniversal Critical Behavior

Liquid crystals in two dimensions undergo a first-order isotropic-to-quasi-nematic transition, provided the particle interactions are sufficiently "sharp and narrow." This implies phase coexistence between isotropic and quasi-nematic domains, separated by interfaces. The corresponding line tension is determined and shown to be very small, giving rise to strong interface fluctuations. When the interactions are no longer "sharp and narrow," the transition becomes continuous, with nonuniversal critical behavior obeying hyperscaling and approximately resembling the two-dimensional Potts model.