Phase equilibria and critical phenomena in closed reactive systems

It is shown that the interplay between chemical reactions and criticality gives rise to some novel phenomena manifested both in a change of critical indices and in some pecularities in the course of chemical reactions. To cite a single example, one can mention the existence of a single point on the hypersurface of the diffusion instability where the slowing down of chemical reactions occurs. The requirements for phase separation in reactive systems are illustrated on simple models of a nonelectrolytic binary mixture and a ternary mixture including electrolytes. The general criterion for the existence of azeotropic points and the upper (lower) critical solution temperatures in reactive systems is formulated. The influence of a chemical reaction on the form of the solubility curve near the melting point in a binary and a dilute ternary mixture is analyzed in detail. A new general approach is formulated to the decay of metastable state in reactive systems. Finally, some possible experimental verifications are considered.This article is a tribute to my dear colleague C. Domb, who has done so much in the understanding of phase transitions and critical phenomena. It is a great pleasure to contribute to this volume honoring him on the occasion of his official retirement.     

Mesodroplet Heterogeneity of Low-Concentration Aqueous Solutions of Polar Organic Compounds

It is found experimentally that a mesoscopic droplet phase is formed in low-concentration aqueous solutions of various polar organic compounds, which are considered in the chemical literature as infinitely soluble in water. The content of dissolved organic molecules in droplets is much higher than in the ambient solution. The droplet size increases with temperature. Theory can explain the mesodroplet formation by the phase separation of a binary mixture affected by the dichotomous noise of twinkling hydrogen bonds between molecules of organic compound and water. The Snyder polarity index, which is used by chemists as a miscibility criterion for molecular compounds, depends in the model on the dipole moments of mixed molecules and the energy and number of hydrogen bonds. With this refinement, it can be used as an estimation criterion for the existence and intensity (i.e., the number of droplets per unit volume of organic aqueous solution) of mesodroplet separation.

     

Stationary dark localized modes: discrete nonlinear Schrödinger equations

Various kinds of stationary dark localized modes in discrete nonlinear Schr?dinger equations are considered. A criterion for the existence of such excitations is introduced and an estimation of a localization region is provided. The results are illustrated in examples of the deformable discrete nonlinear Schr?dinger equation, of the model of Frenkel excitons in a chain of two-level atoms, and of the model of a one-dimensional Heisenberg ferromagnetic in the stationary phase approximation. The three models display essentially different properties. It is shown that at an arbitrary amplitude of the background it is impossible to reach strong localization of dark modes. In the meantime, in the model of Frenkel excitons, exact dark compacton solutions are found.     

Quantum diffusions and the noncommutative torus

Quantum diffusions driven by the creation and annihilation processes on the noncommutative torus algebra are considered. A cohomological obstruction to the existence of such a diffusion is overcome by constructing a diffusion on a larger algebra. There are implications for models in solid-state physics based on the noncommutative torus.     

Electron charge ordering in the extended Hubbard model

The Hubbard model on 3-dimensionalsc lattice with an attractive or repulsive on site interaction, augmented by a renulsive nearest neighbour interaction and its atomic limit are studied using the method of infrared bounds. Conditions upon interactions for the existence of a temperature driven phase transition to so called charge ordered phase are derived. A lower bound in terms of interactions for the corresponding critical temperature is calculated.     

Slow coarsening in a class of driven systems

The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher dimensions. In particular we study a system of three types of particles that diffuse under local conserving dynamics in two dimensions. Arguments and numerical studies are presented indicating that the coarsening process in any number of dimensions is logarithmically slow in time. A key feature of this behavior is that the interfaces separating the various growing domains are macroscopically smooth (well approximated by a Fermi function). This implies that the coarsening mechanism in one dimension is readily extendible to higher dimensions. Received 3 April 2000     

Flexomagnetoelectric interaction in multiferroics

We present a theoretical analysis of phase separation in the presence of a spatially periodic forcing of wavenumber q traveling with a velocity v. By an analytical and numerical study of a suitably generalized 2d-Cahn-Hilliard model we find as a function of the forcing amplitude and the velocity three different regimes of phase separation. For a sufficiently large forcing amplitude a spatially periodic phase separation of the forcing wavenumber takes place, which is dragged by the forcing with some phase delay. These locked solutions are only stable in a subrange of their existence and beyond their existence range the solutions are dragged irregularly during the initial transient period and otherwise rather regular. In the range of unstable locked solutions a coarsening dynamics similar to the unforced case takes place. For small and large values of the forcing wavenumber analytical approximations of the nonlinear solutions as well as for the range of existence and stability have been derived.     

Scaling law in the ordering process of quenched thermodynamically unstable systems

The dynamics of phase separation in quenched thermodynamically unstable systems is studied. The scaling law exhibited in the late stage of the ordering process is investigated by the interface model. In the kinetics of the order-disorder transition the motion of random interfaces is shown to be responsible for the scaling law. The scaling form of the scattering function is obtained with particular attention to the fluctuating thermal noises. A droplet picture is used to discuss spinodal decomposition of off-critically quenched binary fluids. The sealing function is calculated explicitly in the region where the Brownian coagulation is most dominant for the phase separation. It is shown that the thermal noises are relevant to the scaling law in the ordering process driven by the Brownian coagulation whereas they are negligible in the kinetics of order-disorder transition.     

Critical phenomena with convergent series expansions in a finite volume

Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish first- from second-order transitions within a finite-size scaling analysis. The criterion applies also to other methods for investigating the phase structure, such as Monte Carlo simulations. Our computational tools are illustrated with the example of scalar (O(N) models with four- and six-point couplings forN=1 andN=4 in three dimensions. It is shown how to localize the tricritical line in these models. We indicate some further applications of our methods to the electroweak transition as well as to models for superconductivity.     

Phase separation in binary systems with internal multiplicative noise

A study of a phase separation process in stochastic systems with a field dependent kinetic coefficient and an internal multiplicative noise is presented. Dynamics of spinodal decomposition at early and late stages is investigated by computer simulations where the domain growth law is generalized. A mean field approach was carried out in order to obtain the stationary probability, bifurcation and phase diagrams displaying reentrant phase transitions. We relate our approach to entropy driven phase transitions theory.     

Melonic Phase Transition in Group Field Theory

Group field theories have recently been shown to admit a 1/N expansion dominated by so-called ‘melonic graphs’, dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher-dimensional generalization of the Kirchhoff tree-matrix theorem. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov–Ooguri models, which describe topological BF theories and are the basis for the construction of 4-dimensional models of quantum gravity.     

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     

Exact thermodynamics of pairing and charge–spin separation crossovers in small Hubbard nanoclusters

The exact numerical diagonalization and thermodynamics in an ensemble of small Hubbard clusters in the ground state and finite temperatures reveal intriguing insights into the nascent charge and spin pairings, Bose condensation and ferromagnetism in nanoclusters. The phase diagram off half filling strongly suggests the existence of quantum critical points and subsequent transitions from electron pairing into unsaturated and saturated ferromagnetic Mott–Hubbard like insulators, driven by electron repulsion. Rigorous criteria for the existence of quantum critical points and crossover temperatures are formulated. The phase diagram for 2×4$2\times 4$-site clusters illustrates how these features are scaled with cluster size. The phase separation and electron pairing, monitored by a magnetic field and electron doping, surprisingly resemble phase diagrams in the family of doped high-Tc$T_c$ cuprates.     

One-dimensional phase transitions in a two-dimensional optical lattice

A phase transition for bosonic atoms in a two-dimensional anisotropic optical lattice is considered. If the tunnelling rates in two directions are different, the system can undergo a transition between a two-dimensional superfluid and a one-dimensional Mott insulating array of strongly coupled tubes. The connection to other lattice models is exploited in order to better understand the phase transition. Critical properties are obtained using quantum Monte Carlo calculations. These critical properties are related to correlation properties of the bosons and a criterion for commensurate filling is established.     

Strong phase separation in a model of sedimenting lattices

We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a one-dimensional lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels- hence the term strong phase separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.     

Phase separation in mixtures of hard core bosons

A theoretical investigation of boson versions of the t-J and t-J(z) models on the square lattice is carried out. In the t-J(z) model, phase separation between a hole-rich and a hole-free phase occurs, at sufficiently low hole doping, for arbitrarily small values of J(z). The boson t-J model, instead, features a uniform ground state at any doping for J/t< or =1.5. No evidence of a striped ground state is found. Relevance of this study to the corresponding fermion models is discussed. Fermi statistics is found to enhance the tendency toward phase separation; in particular, phase separation is predicted, at low doping, in the fermion t-J(z) model, at all values of J(z).     

Phase separation and coarsening in electrostatically driven granular media

A continuum model for the phase separation and coarsening in electrostatically driven granular media is formulated in terms of a Ginzburg-Landau equation subject to conservation of the total number of grains. In the regime of well-developed clusters, the continuum model is used to derive "sharp-interface" equations that govern the dynamics of the interphase boundary. The model captures the essential physics of this system.     

Convective Cahn-Hilliard models: from coarsening to roughening

In this paper we demonstrate that convective Cahn-Hilliard models, describing phase separation of driven systems (e.g., faceting of growing thermodynamically unstable crystal surfaces), exhibit, with the increase of the driving force, a transition from the usual coarsening regime to a chaotic behavior without coarsening via a pattern-forming state characterized by the formation of various stationary and traveling periodic structures as well as structures with localized oscillations. Relation of this phenomenon to a kinetic roughening of thermodynamically unstable surfaces is discussed.