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Spontaneous onset of a low temperature topologically ordered phase in a 2-dimensional (2D) lattice model of uniaxial liquid crystal (LC) was debated extensively pointing to a suspected underlying mechanism affecting the RG flow near the topological fixed point. A recent MC study clarified that a prior crossover leads to a transition to nematic phase. The crossover was interpreted as due to the onset of a perturbing relevant scaling field originating from the extra spin degree of freedom. As a counter example and in support of this hypothesis, we now consider V-shaped bent-core molecules with rigid rod-like segments connected at an assigned angle. The two segments of the molecule interact with the segments of all the nearest neighbours on a square lattice, prescribed by a biquadratic interaction. We compute equilibrium averages of different observables with Monte Carlo techniques as a function of temperature and sample size. For the chosen molecular bend angle and symmetric inter-segment interaction between neighbouirng molecules, the 2D system shows two transitions as a function of T: the higher one at T1 leads to a topological ordering of defects associated with the major molecular axis without a crossover, imparting uniaxial symmetry to the medium described by the first fundamental group of the order parameter space $pi_{1}$= $Z_{2}$ (inversion symmetry). The second at T2 leads to a medium displaying biaxial symmetry with $pi_{1}$ = Q (quaternion group). The biaxial phase shows a self-similar microscopic structure with the three axes showing power law correlations with vanishing exponents as the temperature decreases.
Using event driven molecular dynamics simulations, we study a three dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of
We consider an off-lattice liquid crystal pair potential in strictly two dimensions. The potential is purely repulsive and short-ranged. Nevertheless, by means of a single parameter in the potential, the system is shown to undergo a first-order phase
Liquid-liquid phase transition (LLPT) in supercooled water has been a long-standing controversial issue. We show simulation results of real stable first-order phase transitions between high and low density liquid (HDL and LDL)-like structures in conf
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