Plate-Nematic Phase in Three Dimensions

  title={Plate-Nematic Phase in Three Dimensions},
  author={Margherita Disertori and Alessandro Giuliani and Ian Jauslin},
  journal={Communications in Mathematical Physics},
  pages={327 - 356}
We consider a system of anisotropic plates in the three-dimensional continuum, interacting via purely hard core interactions. We assume that the particles have a finite number of allowed orientations. In a suitable range of densities, we prove the existence of a uni-axial nematic phase, characterized by long range orientational order (the minor axes are aligned parallel to each other, while the major axes are not) and no translational order. The proof is based on a coarse graining procedure… 

Nematic first order phase transition for liquid crystals in the van der Waals–Kac limit

In this paper we revisit and extend some mathematical aspects of Onsager's theory of liquid crystals that have been investigated in recent years by different communities (statistical mechanics,

Entropy of fully packed hard rigid rods on d-dimensional hypercubic lattices.

It is conjecture, based on a perturbative series expansion, that this large-k behavior of entropy per site is superuniversal and continues to hold on all d-dimensional hypercubic lattices, with d≥2.

Columnar order in random packings of $2\times2$ squares on the square lattice

We study random packings of 2×2 squares with centers on the square lattice Z, in which the probability of a packing is proportional to λ to the number of squares. We prove that for large λ, typical



The Nematic Phase of a System of Long Hard Rods

We consider a two-dimensional lattice model for liquid crystals consisting of long rods interacting via purely hard core interactions, with two allowed orientations defined by the underlying lattice.

Lattice models for liquid crystals

A problem in the theory of liquid crystals is to construct a model system which at low temperatures displays long-range orientational order, but not translational order in all directions. We present

Entropy-Driven Phase Transition in a Polydisperse Hard-Rods Lattice System

We study a system of rods onℤ2, with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct

On the orientational ordering of long rods on a lattice

We argue that a system of straight rigid rods of length k on a square lattice with only hard-core interactions shows two phase transitions as a function of density ρ for k ⩾ 7. The system undergoes a

Nematic Liquid Crystal Phase in a System of Interacting Dimers and Monomers

We consider a monomer-dimer system with a strong attractive dimer-dimer interaction that favors alignment. In 1979, Heilmann and Lieb conjectured that this model should exhibit a nematic liquid

Biaxial nematic phase in bent-core thermotropic mesogens.

The unique low-angle x-ray diffraction patterns in the nematic phases exhibited by three rigid bent-core mesogens clearly reveal their biaxiality.

Thermotropic biaxial nematic liquid crystals.

Polarized microscopy and conoscopy indicate that liquid crystal mesogens based on a nonlinear oxadiazole unit that exhibit nematic phases near 200 degrees C are biaxial nematics, and unambiguous and quantitative evidence for biaXiality is achieved using 2H NMR spectroscopy.

Thermotropic biaxial nematic phase in liquid crystalline organo-siloxane tetrapodes.

Infrared absorbance measurements have been carried out on two liquid crystalline organo-siloxane tetrapodes. Results unambiguously show the existence of a biaxial nematic phase below a uniaxial