Three-dimensional immiscible lattice gas: Application to sheared phase separation

A new lattice-gas cellular automaton model for simulating binary fluids in three dimensions is introduced. It is particularly suitable for modeling slow flows of mixtures with complicated interface geometries or within complicated boundaries, such as in the interior of a porous rock. Phase separation is triggered spontaneously in the model by statistical fluctuations and phase domains are approximately isotropic. The measured surface tension is large compared to that in analogous two-dimensional models. The model is applied to a study of the time-dependent effective viscosity of a phase-separating mixture in a simple shear flow. Results qualitatively match both experiment and theory: the viscosity increases rapidly, then decays gradually to a steady-state value which is larger than the viscosity of the pure fluids. The effective viscosity increases with increasing concentration and decreases with increasing strain rate.     

Existence of several surface-reconstructed phases in a two-dimensional lattice model

The zero-temperature phase diagram is rigorously obtained for a two-dimensional lattice model with four energy parameters. It is shown that the parameter space can be divided into regions, together with their boundaries, such that in each region the ground-state configurations are of one of seven different types. These types include one which is nondegenerate, four which are doubly degenerate, one which is infinitely degenerate but with no residual entropy, and one which is infinitely degenerate and has a nonzero residual entropy. The Pirogov-Sinai extension of the Peierls argument is used to establish the existence at low temperatures of four different types of ordered surface-reconstructed phases.     

A first-order phase transition in a three-dimensional vertex model

For a specific three-dimensional vertex model, it is proven that it will show a first-order phase transition. The critical temperature is given in terms of the energy of some local vertex configurations. The approach used is similar to the Nagle approach. Some classes of compounds are considered which may be related to this model.     

Phase separation in a three-dimensional,two-phase,hydrodynamic lattice gas

The dynamics of phase separation is explored using an immiscible 3D lattice-gas model. Scaling laws for the growth rate and power spectraS(k) of the growth patterns are computed. For small wavenumbersS(k) shows a crossover fromk ² tok ⁴ behavior. The theoretical prediction for the asymptotic domain growthRt ^2/3 is supported by our results. We discuss the possibility to observe an intermediatet scaling. We show the influence of hydrodynamic forces in symmetric and asymmetric mixtures by comparing simulations with and without momentum conservation. The structure functionS(k) is not significantly modified by hydrodynamics, but the growth rate changes clearly. As a general result, it is shown that, in spite of the unusual thermodynamics of this model, many characteristics of the growth dynamics are surprisingly in agreement with the classical theoretical and experimental results.     

Renormalization group study of a three-dimensional lattice model with directional bonding

We consider a bcc lattice model in which each site is either vacant or occupied by a molecule. The molecules have four symmetrically arranged arms directed towards four of the eight nearest-neighbor sites. Two molecules form a bond if they have bonding arms pointing towards each other and along their line of centers. We introduce bonding energies as well as two-, three-, and four-molecule interactions. The model is studied using a real-space renormalization group method. The form of the pressure-temperature phase diagram is found to be very sensitive to small changes in the relative sizes of the energy parameters. Adjustment of these parameters allows us to obtain a phase diagram which resembles that of the ice-water-steam system. The nature of the transitions between the various ordered phases is examined and the critical exponents are obtained.     

Frustration and quantum phase transitions in an anisotropic antiferromagnet on a square lattice

We study the effect of frustration between nearest and next-nearest neighbors of the quantum S=1 anisotropic Heisenberg model on a square lattice using the bond operator technique. A single-site anisotropy term induces a quantum phase transition in the system. We calculate the effect of zero-temperature quantum fluctuations on the magnetization for the Néel and collinear antiferromagnetic phases.     

Phase diagram for a lattice model for confining bags

Summary The two 1-dimensional spin systems proposed by Aharonov and Schwartz as models of confinement isomorphic with the MIT bag model are thoroughly analysed by using an improved mean-field scheme (which has the customary mean-field theory as its zero-th-order approximation), recently suggested to deal with fluctuation in a perturbative cluster-cumulant aproach. The ground state and its phase diagram are discussed in detail.

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Riassunto I due modelli di spin unidimensionali proposti da Aharonov e Schwartz come modelli di confinamento isomorfi al ?MIT bag model? sono analizzati compiutamente mediante uno schema di campo medio migliorato (che ammette l’ordinaria teoria di campo medio come approssimazione di ordine zero), elaborato recentemente per trattare le fluttuazioni con un approccio perturbativo che utilizza il calcolo dei cumulanti su grappoli. Lo stato fondamentale ed il corrispondente diagramma di fase sono discussi in dettaglio.

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Реэюме Проводится аналиэ двух одномерных спиновых систем, предложенных Аароновым и Щварцем в качестве моделей удержания, иэоморфного в случае MIT-модели ?мешка?. Для аналиэа исполыэуется усовершенствованная схема среднего поля (в которой обычная теория среднего поля чредставляет приближение нулевого порядка). Эта схема была недавно предложена для рассмотрения флуктуаций в пертурбационном кластерном подходе. Подробно обсуждаются основное состояние и соответствуюшая фаэовая диаграмма.

     

三维颗粒气体相分离现象

颗粒体系是一类复杂的耗散体系.在颗粒气体中,耗散性质会使其内部形成局部的凝聚,类似于真实气体中亚稳分解形成的液滴,因此被认为是颗粒气液两相分离的过程. 零重力环境下二维颗粒气体相分离现象已有成熟的流体静力学理论解释,将该理论模型推广到三维情形,发现相分离现象依然存在且具有同样的不稳定性根源,通过理论计算给出了三维相分离发生的具体条件. 同时,用分子动力学方法模拟检验了理论结果,并给出了三维颗粒气体相分离的新形貌. 关键词： 颗粒气体 耗散 相分离 分子动力学模拟     

Non-equilibrium phase transition of the fully frustrated square lattice Coulomb gas model

The non-equilibrium phase transitions of the fullyfrustrated (f = 1/2) square lattice Coulomb gas (CG) modeldriven by external electrical fields are studied in the frameworkof the short-time dynamic scaling approach. The criticaltemperature T_c, the static and dynamic critical exponents2β/ν, ν, and z are obtained for several smalldriving fields. The results show that T_c decreases with theincrease of electric field, and 2β/ν and z arestrongly dependent on the external electric field. Interestingly,contrary to the equilibrium case, in the presence of smallelectric field, the calculated exponent ν is close to that inpure 2D Ising model, which provides numerical evidence thatexternal electric field may change the universality class of thef = 1/2 CG system.     

Phase transitions in lattice gas models for water

Water-like lattice gases on the triangular and body-centered cubic lattices are investigated. Molecules may reside on the lattice sites in either of two possible orientations, a hydrogen bond being formed between molecules on neighboring sites if they have the proper orientation with respect to one another. For a range of chemical potential at sufficiently low temperatures, the models are shown to have an ordered phase consisting of an open, hydrogen-bonded, icelike structure. The models are shown to be transitionfree at sufficiently high temperature, indicating the existence of a critical point.Research supported in part by the U.S. National Science Foundation, Grant CHE-7726177, and by The Robert A. Welch Foundation, Grant P-446.     

Power-law falloff in the kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas

We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperaturegb and a constant >0 such that for all> and all external charges R we have , whereG (x) is the two-point external charges correlation function,=dist(, Z), and for 0$$ " align="middle" border="0"> . In the case of a hard-core or standard Coulomb gas with activityz, we may choose=(z) such that(z)24 asz0.     

Phase transitions in a driven lattice gas at two temperatures

By suitably combining the uniformly driven lattice gas and the two-temperature kinetic Ising model, we obtain a generalized model that allows us to probe a variety of nonequilibrium phase transitions, including a type not previously observed. This new type of transition involves longitudinally ordered steady states, which are phase-segragated states with interface normalsparallel to the drive. Using computer simulations on a two-dimensional lattice gas, we map out the structure of the phase diagram, and the nature of the transitions, in the three-dimensional space of the drive and the two temperatures. While recovering anticipated results in most cases, we find one surprise, namely, that the transition from disorder to longitudinal order is continuous. Unless it turns out to be very weakly first order, this result is inconsistent with the expectation of field-theoretic renormalization group calculations.     

Phase transitions in a driven lattice gas in two planes

We report on a Monte Carlo study of ordering in a nonequilibrium system. The system is a lattice gas that comprises two equal, parallel square lattices with stochastic particle-conserving irreversible dynamics. The particles are driven along a principal direction under the competition of the heat bath and a large, constant external electric field. There is attraction only between particles on nearest-neighbor sites within the same lattice. Particles may jump from one plane to the other; therefore, density fluctuations have an extra mechanism to decay and build up. It helps to obtain the steady-state accurately. Spatial correlations decay with distance according to a power law at high enough temperature, as for the ordinary two-dimensional case. We find two kinds of nonequilibrium phase transitions. The first one has a critical point for half occupation of the lattice, and seems to be related to the anisotropic phase transition reported before for the plane. This transition becomes discontinuous for low enough density. The difference of density between the planes changes discontinuously for any density at a lower temperature. This seems to correspond to a phase transition that does not have a counterpart in equilibrium nor in the two-dimensional nonequilibrium case.     

Diffusion anomaly in a three-dimensional lattice gas

We investigate the relationship between thermodynamic and dynamic properties of an associating lattice-gas (ALG) model. The ALG combines a three-dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of freedom. The competition between the directional attractive forces and the soft core potential results in two liquid phases, double criticality and density anomaly. We study the mobility of the molecules in this model by calculating the diffusion constant at a constant temperature, D. We show that D has a maximum at a density ρ_max and a minimum at a density ρ_min<ρ_max. Between these densities the diffusivity differs from the one expected for normal liquids. We also show that in the pressure-temperature phase-diagram the line of extrema in diffusivity is close to the liquid-liquid critical point and it is partially inside the temperature of maximum density (TMD) line.     

Magnetic phase structure on the Penrose lattice

The Ising model on a two-dimensional Penrose tiling is studied by means of the Migdal-Kadanoff scheme. This approximate renormalization method closely follows the inflation rules of the tiling, which are easily described in terms of Robinson triangles, and lead to the consideration of four types of nearest neighbor couplings. The ferromagnetic phase transition is similar to the usual one encountered on periodic lattices. When the couplings have both signs, the presence of frustration without randomness yields a fairly intricate phase diagram, essentially made up of two regions with a very complicated border. Region I consists of quasiferromagnetic models, which exhibit long-range order below some finite critical temperature. The models of region II are paramagnetic at nonzero (low) temperature, but may become ordered (reen-trant phases) in a higher temperature range.     

Reentrant phase transitions and multicompensation points in the mixed-spin Ising ferrimagnet on a decorated Bethe lattice

A mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by combining the decoration–iteration transformation with the method of exact recursion relations. Exact results for critical lines, compensation temperatures, total and sublattice magnetizations are obtained from a precise mapping relationship with the corresponding spin-1/2 Ising model on a simple (undecorated) Bethe lattice. The effect of next-nearest-neighbour interaction and single-ion anisotropy on magnetic properties of the ferrimagnetic model is investigated in particular. It is shown that the total magnetization may exhibit multicompensation phenomenon and the critical temperature vs. the single-ion anisotropy dependence basically changes with the coordination number of the underlying Bethe lattice. The possibility of observing reentrant phase transitions is related to a high enough coordination number of the underlying Bethe lattice.     

A model of natural selection that exhibits a dynamic phase transition

A simple, stochastic model is developed of an asexual biological population that is undergoing natural selection. It is then observed that the size of the population, like the temperature parameter in the simulated annealing algorithm, is a measure of the amount of randomness to be allowed in the system. Exploiting the formal analogy between the two processes, it is shown that the distribution of different types of organisms in the population model converges to a stationary distribution if the population is growing more slowly thanO(lnt) (annealing), but can fail to converge at all if the population is growing faster thanO(lnt) (quenching). The results may be related to the historical accidents that permeate biological structures.     

Simulating liquid-vapor phase separation under shear with lattice Boltzmann method

We study liquid-vapor phase separation under shear via the Shan-Chen lattice Boltzmann model. Besides the rheological characteristics, we analyze the Kelvin-Helmholtz (K-H) instability resulting from the tangential velocity difference of the fluids on two sides of the interface. We discuss also the growth behavior of droplets. The domains being close to the walls are lamellar-ordered, where the hydrodynamic effects dominate. The patterns in the bulk of the system are nearly isotropic, where the domain growt...