Phase Transition of Mobile Potts Model for Liquid Crystals

Phase transitions in liquid crystals have been intensively studied during the last 40 years due to their numerous daily technological applications. We study by Monte-Carlo simulations the phase transitions in liquid crystals as function of molecule concentration and temperature. The molecule are represented by a 6-state Potts model on a simple cubic lattice, where each crystalline direction is assigned to a Potts value. Molecules can go from a lattice site to another one. We take into account an attractive interaction between nearest neighboring molecules. At low temperature, molecules form an ordered solid phase. As the temperature increases, molecules at the surface are detached from the solid to go to the empty space. Depending on the ratio of the solid phase volume to the whole volume, namely the concentration, we can have first order transition or second order transition and even, for the dilute case, no transition at all. The physical mechanism of each kind of transitions are analyzed.