The nematic-disordered phase transition in systems of long rigid rods on two dimensional lattices (original) (raw)
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Phase transition from nematic to high-density disordered phase in a system of hard rods on a lattice
Physical Review E, 2022
A system of hard rigid rods of length k on hypercubic lattices is known to undergo two phase transitions when chemical potential is increased: from a low density isotropic phase to an intermediate density nematic phase, and on further increase to a high-density phase with no orientational order. In this paper, we argue that, for large k, the second phase transition is a first order transition with a discontinuity in density in all dimensions greater than 1. We show that the chemical potential at the transition is ≈ k ln[k/ ln k] for large k, and that the density of uncovered sites drops from a value ≈ (ln k)/k 2 to a value of order exp(−ak), where a is some constant, across the transition. We conjecture that these results are asymptotically exact, in all dimensions d ≥ 2. We also present evidence of coexistence of nematic and disordered phases from Monte Carlo simulations for rods of length 9 on the square lattice.
Sequence of phase transitions in a model of interacting rods
Physical review, 2022
In a system of interacting thin rigid rods of equal length 2 on a two-dimensional grid of lattice spacing a, we show that there are multiple phase transitions as the coupling strength κ = /a and the temperature are varied. There are essentially two classes of transitions. One corresponds to the Ising-type spontaneous symmetry breaking transition and the second belongs to less-studied phase transitions of geometrical origin. The latter class of transitions appear at fixed values of κ irrespective of the temperature, whereas the critical coupling for the spontaneous symmetry breaking transition depends on it. By varying the temperature, the phase boundaries may cross each other, leading to a rich phase behaviour with infinitely many phases. Our results are based on Monte Carlo simulations on the square lattice, and a fixed-point analysis of a functional flow equation on a Bethe lattice.
Physical Review Letters, 2018
The presence of stable topological defects in a two-dimensional (d = 2) liquid crystal model allowing molecular reorientations in three dimensions (n = 3) was largely believed to induce defectmediated Berzenskii-Kosterlitz-Thouless (BKT) type transition to a low temperature phase with quasi long-range order. However, earlier Monte Carlo (MC) simulations could not establish certain essential signatures of the transition, suggesting further investigations. We study this model by computing its equilibrium properties through MC simulations, based on the determination of the density of states of the system. Our results show that, on cooling, the high temperature disordered phase deviates from its initial progression towards the topological transition, crossing over to a new fixed point, condensing into a nematic phase with exponential correlations of its director fluctuations. The thermally induced topological kinetic processes continue, however limited to the length scales set by the nematic director fluctuations, and lead to a second topological transition at a lower temperature. We argue that in the (d = 2, n = 3) system with a biquadratic Hamiltonian, the presence of additional molecular degree of freedom and local Z2 symmetry associated with lattice sites, together promote the onset of an additional relevant scaling field at matching length scales in the high temperature region, leading to a crossover.
Physical Review E, 2009
Monte Carlo simulations have been carried out for a system of monomers on square lattices that, by decreasing temperature or increasing density, polymerize reversibly into chains with two allowed directions and, at the same time, undergo a continuous isotropic-nematic (IN) transition. The results show that the self-assembly process affects the nature of the transition. Thus, the calculation of the critical exponents and the behavior of Binder cumulants indicate that the universality class of the IN transition changes from two-dimensional Ising-type for monodisperse rods without self-assembly to q = 1 Potts-type for self-assembled rods. PACS numbers: 05.50.+q, 64.70.mf, 61.20.Ja, 64.75.Yz, 75.40.Mg Self-assembly is a challenging field of research, driven principally by the desire to design new materials. Moreover, self-assembly is used permanently in biological systems to construct supramolecular structures such as virus capsids, filaments, and many others large molecular complexes. So, understanding the rules of self-assembly has important applications to both materials science and biology [1].
Nematic phase in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:mrowmml:msubmml:miJmml:mn1mml:mtext−mml:msubmml:miJmml:mn2square-lattice Ising model in an external field
Physical Review E, 2015
The J1-J2 Ising model in the square lattice in the presence of an external field is studied by two approaches: the Cluster Variation Method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter κ = J2/|J1| which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.
Nonlinear interaction effect on the phase distribution in one-dimensional disordered lattices
Journal of Physics: Condensed Matter, 1999
We studied in this paper the effect of nonlinear interaction on the PD of a onedimensional Kronig-Penney chain. In the quasi-ballistic regime (L (2k F ) −1 λ (localization length)), an attractive nonlinear potential leads to a smooth peak with an oscillatory shift in its position, while for repulsive potentials the peak becomes sharper and moves towards π . In the quasi-metallic regime ((2k F ) −1 L λ), the uniform PD becomes peaked as we increase the nonlinear potential. Depending on the sign of the nonlinear potential, this peak moves either away from or closer to π. In the strong disorder regime, the nonlinearity plays an identical role to disorder. It was found that the overall effect of nonlinear interaction in the mixed disorder case can be interpreted as a superposition of those for potential barriers and wells treated separately. Further results and discussion are also provided.
Phase transitions in a system of hard Y-shaped particles on the triangular lattice
Physical Review E, 2018
We study the different phases and the phase transitions in a system of Y-shaped particles, examples of which include Immunoglobulin-G and trinaphthylene molecules, on a triangular lattice interacting exclusively through excluded volume interactions. Each particle consists of a central site and three of its six nearest neighbours chosen alternately, such that there are two types of particles which are mirror images of each other. We study the equilibrium properties of the system using grand canonical Monte Carlo simulations that implements an algorithm with cluster moves that is able to equilibrate the system at densities close to full packing. We show that, with increasing density, the system undergoes two entropy-driven phase transitions with two broken-symmetry phases. At low densities, the system is in a disordered phase. As intermediate phases, there is a solid-like sublattice phase in which one type of particle is preferred over the other and the particles preferentially occupy one of four sublattices, thus breaking both particle-symmetry as well as translational invariance. At even higher densities, the phase is a columnar phase, where the particle-symmetry is restored, and the particles preferentially occupy even or odd rows along one of the three directions. This phase has translational order in only one direction, and breaks rotational invariance. From finite size scaling, we demonstrate that both the transitions are first order in nature. We also show that the simpler system with only one type of particles undergoes a single discontinuous phase transition from a disordered phase to a solid-like sublattice phase with increasing density of particles.
Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice
Physical Review B, 2011
Frustration has proved to give rise to an extremely rich phenomenology in both quantum and classical systems. The leading behavior of the system can often be described by an effective model, where only the lowest-energy degrees of freedom are considered. In this paper we study a system corresponding to the strong trimerization limit of the spin 1/2 kagome antiferromagnet in a magnetic field. It has been suggested that this system can be realized experimentally by a gas of spinless fermions in an optical kagome lattice at 2/3 filling. We investigate the low-energy behavior of both the spin 1/2 quantum version and the classical limit of this system by applying various techniques. We study in parallel both signs of the coupling constant J since the two cases display qualitative differences. One of the main peculiarities of the J > 0 case is that, at the classical level, there is an exponentially large manifold of lowest-energy configurations. This renders the thermodynamics of the system quite exotic and interesting in this case. For both cases, J > 0 and J < 0, a finitetemperature phase transition with a breaking of the discrete dihedral symmetry group D6 of the model is present. For J < 0, we find a transition temperature T < c /|J| = 1.566 ± 0.005, i.e., of order unity, as expected. We then analyze the nature of the transition in this case. While we find no evidence for a discontinuous transition, the interpretation as a continuous phase transition yields very unusual critical exponents violating the hyperscaling relation. By contrast, in the case J > 0 the transition occurs at an extremely low temperature, T > c ≈ 0.0125 J. Presumably this low transition temperature is connected with the fact that the low-temperature ordered state of the system is established by an order-by-disorder mechanism in this case.
Journal of Statistical Physics, 1987
Two-dimensional lattice-gas models with attractive interactions and particleconserving happing dynamics under the influence of a very large external electric field along a principal axis are studied in the case of a critical density. A finite-size scaling analysis allows the evaluation of critical indexes for the infinite system asβ=0.230±0.003,v=0.55±0.2, and α 0. We also describe some qualitative features of the system evolution and the existence of certain anisotropic order even well above the critical temperature in the case of finite lattices.