Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang–Landau Method

Abstract

We study the nature of the smectic–isotropic phase transition using a mobile 6-state Potts model. Each Potts state represents a molecular orientation. We show that with the choice of an appropriate microscopic Hamiltonian describing the interaction between individual molecules modeled by a mobile 6-state Potts spins, we observe the smectic phase dynamically formed when we cool the molecules from the isotropic phase to low temperatures (T). In order to elucidate the order of the transition and the low-T properties, we use the high-performance Wang–Landau flat energy-histogram technique. We show that the smectic phase goes to the liquid (isotropic) phase by melting/evaporating layer by layer starting from the film surface with increasing T. At a higher T, the whole remaining layers become orientationally disordered. The melting of each layer is characterized by a peak of the specific heat. Such a succession of partial transitions cannot be seen by the Metropolis algorithm. The successive layer meltings/evaporations at low T are found to have a first-order character by examining the energy histogram. These results are in agreement with experiments performed on some smectic liquid crystals.

Vortex structure in magnetic nanodots: Dipolar interaction, mobile spin model, phase transition and melting

“…Note that our technique using the mobile spin model can be used to study the behavior of liquid crystals. We have recently succeeded to obtain the nematic and smectic structures while cooling a liquid to low T using an appropriate choice of Hamiltonian [41,42].…”

Modeling and Analysis of Anomalies in the Network Infrastructure Based on the Potts Model

“…In this case, we are talking about the phase of network cohesion and the phase of inconsistency. However, this algorithm does not refer to the states of individual nodes; therefore, the Potts model was used for the needs of the research [12][13][14]. This model is a generalisation of the Ising model of magnetism [7].…”

“…Thus, this phenomenon is critical. One of the models allowing the analysis of phase transitions is the Ising magnetism model [5][6][7][8][9][10][11] and its generalisation in the form of the Potts model [12][13][14]. The potential of this model in studying the behaviour and properties of IT structures was presented in the author's earlier study [15].…”