A model three-component system is considered in which the bonds of a honeycomb lattice are covered by rodlike molecules of typesAA, BB, andAB. The ends of molecules near a common lattice site interact with energies
AA,
BB, and
AB. The model is equivalent to an Ising model on the 3–12 lattice. Exact results are obtained for the two-phase coexistence curves in the isothermal composition plane. 相似文献
Summary The present work reports Monte Carlo calculations on a classical square lattice, consisting of purely dipolar plane rotators
with identical dipole moments. Dipolar interactions are known not be essential for nematic ordering, but they can play a significant
role in some specific cases; along the lines of the lattice model approximation already used in simulation work on liquid
crystals, our system can be considered as an extreme case of nematogenic potential model. The system possesses an antiferroelectric
ground state and, at higher temperature, it undergoes a transition to an orientationally disordered phase; comparison with
the mean-field treatment of the transition is also reported. The structural properties were investigated by calculating orientational
correlation functions, and found to exhibit some qualitative differences with respect to other potential models previously
investigated for nematics. Simulation results indicate a close qualitative similarity with a three-dimensional analogue investigated
in our previous work.
Riassunto Il presente lavoro riporta calcoli Monte Carlo per un reticolo classico quadrato, costituito da rotatori piani puramente dipolari,
con identici momenti. è noto che le interazioni dipolari non sono essenziali per l'ordinamento nematico, ma esse possono avere
un ruolo significativo in alcuni casi specifici; lungo le linee dell'approssimazione a modello reticolare già applicata in
lavori di simulazione per cristalli liquidi, il nostro sistema può pertanto venire considerato come un caso estremo di modello
di potenziale nematogenico. Il sistema possiede stato fondamentale antiferroelettrico ed, a temperatura piú elevata, transisce
ad una fase orientazionalmente disordinata; si riportano per confronto i risultati della trattazione a campo medio per tale
transizione. Le proprietà strutturali furono investigate calcolando funzioni di correlazione orientazionale, e si è trovato
che esse mostrano qualche differenza qualitativa rispetto ad altri modelli di potenziale previamente studiati per nematici.
I risultati di simulazione indicano una stretta somiglianza qualitativa con un analogo tridimensionale investigato in nostri
precedenti lavori.
Резюме В этой работе предлагаются вычисления по методу Монте-Карло для классической квадратичной решетки, состоящей нз чнсто дипольных
плоских ротаторов с тождественными дипольными моментами. Известно, что дипольные взаимодействия не являются существенными
для нематического упорядочения, но они могут играть существенную роль в некоторых специфических случаях: в частности, в приближении
модельной решетки, уже использованном при моделировании на жидких кристаллах, наша система может рассматриваться как предельный
случай модели немтическочо потенциала. Рассмотренная система обладает антиферромагнитным основным состоянием и при высоких
температурах она претерпевает переход в ориентационно разупорядоченную фазу; также проводится сравнение с рассмотрением этого
перехода с помощью среднего поля. Исследуются структурные свойства, вычисляя ориентационные корреляционные функции. Обнаружено
существование некоторых качественных различий по сравнению с моделями потенциалов, ранее использованных для нематиков. Результаты
моделирования обнаруживают качественное подобие с трехмерным аналогом, исследованным в нашей предыдущей работе.
The phase diagrams of the three-layer Ising model on the honeycomb lattice with a diluted surface have been constructed using the probabilistic cellular automata based on Glauber algorithm. The effects of the exchange interactions on the phase diagrams have been investigated. A general mathematical expression for the critical temperature is obtained in terms of relative coupling r = J1/J and Δs = (Js/J) ? 1, where J and Js represent the nearest neighbor coupling within inner- and surface-layers, respectively, and each magnetic site in the surface-layer is coupled with the nearest neighbor site in the inner-layer via the exchange coupling J1. In the case of antiferromagnetic coupling between surface-layer and inner-layer, system reveals many interesting phenomena, such as the possibility of existence of compensation line before the critical temperature. 相似文献
We use the Monte Carlo method to study an antiferromagnetical Ising spin
system on a centred honeycomb lattice, which is composed of two kinds
of 1/2 spin particles A and B. There exist two different bond
energies JA-A and JA-B in this lattice. Our
study is focused on how the ratio of JA-B to JA-A influences the critical behaviour of this system by analysing the physical quantities, such as the energy, the order parameter,
the specific heat, susceptibility, {etc} each as a function of temperature for a given ratio of JA-B to JA-A. Using these results together with the finite-size scaling method,
we obtain a phase diagram for the ratio JA-B / JA-A. This work is helpful for studying the phase transition
problem of crystals composed of compounds. 相似文献
Spontaneous melting of a perfect crystalline graphene model in 2D space is studied via molecular dynamics simulation. Model containing 104 atoms interacted via long-range bond-order potential (LCBOP) is heated up from 50 to 8,450 K in order to see evolution of various thermodynamic quantities, structural characteristics and occurrence of various structural defects. We find that spontaneous melting of our graphene model in 2D space exhibits a first-order behaviour of the transition from solid 2D graphene sheet into a ring-like structure 2D liquid. Occurrence and clustering of Stone–Wales defects are the first step of melting process followed by breaking of C–C bonds, occurrence/growth of various types of vacancies and multi-membered rings. Unlike that found for melting of a 2D crystal with an isotropic bonding, these defects do not occur homogeneously throughout the system, they have a tendency to aggregate into a region and liquid phase initiates/grows from this region via tearing-like or crack-propagation-like mechanism. Spontaneous melting point of our graphene model occurs at Tm = 7,750 K. The validity of classical nucleation theory and Berezinsky–Kosterlitz–Thouless–Nelson–Halperin–Young (BKTNHY) one for the spontaneous melting of our graphene model in strictly 2D space is discussed. 相似文献
We report on the transport properties of the super‐honeycomb lattice, the band structure of which possesses a flat band and Dirac cones, according to the tight‐binding approximation. The super‐honeycomb model combines the honeycomb lattice and the Lieb lattice and displays the properties of both. It also represents a hybrid fermionic and bosonic system, which is rarely seen in nature. By choosing the phases of input beams properly, the flat‐band mode of the super‐honeycomb lattice will be excited and the input beams will exhibit strong localization during propagation. On the other hand, if the modes of Dirac cones of the super‐honeycomb lattice are excited, one will observe conical diffraction. Furthermore, if the input beam is properly chosen to excite a sublattice of the super‐honeycomb lattice and the modes of Dirac cones with different pseudospins, e.g., by the three‐beam interference pattern, the pseudospin‐mediated vortices will be observed.
The temporal evolution of two-dimensional foam is studied by event-driven numerical simulations based on different types of models. It is shown that most of the dynamical and topological features seen in experimental measurements can be reproduced. The average area of cells scales linearly with time and the distribution of n-sided cells can be compared with known results. The topological models regarding the lengths of the boundaries yield the best results among the models studied. 相似文献
The dissociated core structure of dislocation in two-dimensional triangular lattice is determined by the variational method
within lattice theory. The dissociation effect leads to a narrower core width of partial dislocations than the compact one.
The equilibrium separation between two partial dislocations is not very sensitive to the intrinsic stacking fault energy and
there exists deviation from the intrinsic stacking fault energy criterion in the continuous elastic theory of dislocation.
The relationship between the equilibrium separation and intrinsic stacking fault energy is analogous in lattice theory and
the Peierls-Nabarro model. But the equilibrium separation obtained in lattice theory is wider than that obtained in the Peierls-Nabarro
model for the same intrinsic stacking fault energy.
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