Density Order Parameter Research Articles

Correlated Fluctuations of Structural Indicators Close to the Liquid-Liquid Transition in Supercooled Water.

Multiple numerical studies have unambiguously shown the existence of a liquid-liquid critical point in supercooled states for different numerical models of water, and various structural indicators have been put forward to describe the transformation associated with this phase transition. Here we analyze numerical simulations of near-critical supercooled water to compare the behavior of several of such indicators with critical density fluctuations. We show that close to the critical point most indicators are strongly correlated to density, and some of them even display identical distributions of fluctuations. These indicators probe the exact same free energy landscape, therefore providing a thermodynamic description of critical supercooled water which is identical to that provided by the density order parameter. This implies that close to the critical point, there is a tight coupling between many, only apparently distinct, structural degrees of freedom.

Microscopic insights into the phase transition of poly(N-isopropylacrylamide) in aqueous media: Effects of molecular weight and polymer concentration

We study a temperature (T)-induced phase transition of semi-dilute poly(N-isopropylacrylamide) (pNIPAm) in H2O and D2O, focusing on effects of molecular weight and polymer concentration. We use simultaneous small- and wide-angle x-ray scattering (SWAXS) and dielectric relaxation spectroscopy (DRS). The hydration number Zhyd of pNIPAm is determined by DRS. We observe a gradual decrease of Zhyd with increasing T below TS − 6 K, where TS is the spinodal temperature, and its subsequent steep decrease on approaching TS. This eccentric two-mode dehydration behavior implies strong cooperative nature of hydration/dehydration of the pNIPAm chains. Furthermore, the observed dehydration is coupled to the critical fluctuations manifested by a power-law divergence of the correlation length ξ. The emergence of a low-q interference peak provides evidence that high-density microglobules are formed even far below Ts, where a swollen coil state of polymer chains is generally considered to be predominant. The local number density of the microglobules is almost unchanged below Ts, but then exhibits a step-like increase just above Ts, where most pNIPAm chains are already collapsed. This observation suggests that in addition to the ordinary (macroscopic) density order parameter, the local number density of the microglobules should serve as an additional order parameter monitoring the phase transition of aqueous pNIPAm. The correlation length significantly decreases at higher polymer concentration because of the stronger interpenetration effect between different chains. At higher concentration, ξ converges to similar values independent of molecular weight, which indicates an already congested state of the pNIPAm chains. Lowering averaged molecular weight leads to a stronger tendency of inter-chain aggregation and interface formation especially at high T.

Microglobule formation and a microscopic order parameter monitoring the phase transition of aqueous poly( N -isopropylacrylamide) solution

The coil-to-globule transition of poly($N$-isopropylacrylamide) (pNIPAm) in water is generally believed to be driven by hydrophobic interaction between the isopropyl groups of its side chains. However, it is still unclear how dehydration and critical fluctuations of the polymer chains are correlated. Here, we use small- and wide-angle x-ray scattering and dielectric relaxation spectroscopy to cover a wide range of the relevant length and time scales, enabling us to grasp an overall picture of this phase transition. We find that the hydration number of pNIPAm decreases only moderately with temperature up to about 6 K below its spinodal temperature ${T}_{\mathrm{S}}$, but then drops steeply on approaching ${T}_{\mathrm{S}}$. This rapid dehydration is coupled to a mean-field-like power-law divergence of the correlation length $\ensuremath{\xi}$, representing fluctuations of the density order parameter. Real-space decoding of an observed interference peak reveals partial-globule formation even far below ${T}_{\mathrm{S}}$ and demonstrates that the polymer-rich phase above ${T}_{\mathrm{S}}$ can be understood as a high-density assembly of the microglobules. Strikingly, condensation of the microglobules and the divergence of $\ensuremath{\xi}$ do not run parallel. Instead, the condensation occurs only above ${T}_{\mathrm{S}}$ and is completed about 6 K above ${T}_{\mathrm{S}}$. The local number density of the microglobules, exhibiting a steplike increase just above ${T}_{\mathrm{S}}$, should be identified as an additional microscopic order parameter governing the phase transition of pNIPAm.

Conditions for l=1 Pomeranchuk instability in a Fermi liquid

We perform a microscropic analysis of how the constraints imposed by conservation laws affect $q=0$ Pomeranchuk instabilities in a Fermi liquid. The conventional view is that these instabilities are determined by the static interaction between low-energy quasiparticles near the Fermi surface, in the limit of vanishing momentum transfer $q$. The condition for a Pomeranchuk instability is set by $F^{c(s)}_l =-1$, where $F^{c(s)}_l$ (a Landau parameter) is a properly normalized partial component of the anti-symmetrized static interaction $F(k,k+q; p,p-q)$ in a charge (c) or spin (s) sub-channel with angular momentum $l$. However, it is known that conservation laws for total spin and charge prevent Pomeranchuk instabilities for $l=1$ spin- and charge- current order parameters. Our study aims to understand whether this holds only for these special forms of $l=1$ order parameters, or is a more generic result. To this end we perform a diagrammatic analysis of spin and charge susceptibilities for charge and spin density order parameters, as well as perturbative calculations to second order in the Hubbard $U$. We argue that for $l=1$ spin-current and charge-current order parameters, certain vertex functions, which are determined by high-energy fermions, vanish at $F^{c(s)}_{l=1}=-1$, preventing a Pomeranchuk instability from taking place. For an order parameter with a generic $l=1$ form-factor, the vertex function is not expressed in terms of $F^{c(s)}_{l=1}$, and a Pomeranchuk instability does occur when $F^{c(s)}_1=-1$. We argue that for other values of $l$, a Pomeranchuk instability occurs at $F^{c(s)}_{l} =-1$ for an order parameter with any form-factor

Frequency Dependencies of the Exchange Spin Wave Reflection Coefficient on a One-Dimensional Magnon Crystal with Complex Interfaces

Background. This work is devoted to theoretical study of the behavior of spin waves passing through multilayer ferromagnetic with complex interfaces. Objective. T he aim of the paper is to calculate the reflection coefficient of multilayer ferromagnetic with complex interfaces as function of spin wave frequency at variable material parameter and constant value of external magnetic field. The formalism of geometric optics allows describing the spin wave refraction process and the reflection coefficient, as well as controlling this process by changing the frequency of the spin wave for given parameters of the medium. Methods. To find the reflection coefficient from a multilayer ferromagnetic the mathematical apparatus of geometric optics was used . To describe the dynamics of the magnetization vector the formalism of the spin density order parameter was used allowing for the use of methods of quantum mechanics to calculate the reflection coefficient from a semi-infinite multilayer structure. Results. The spin wave reflection coefficient of semi-infinite multilayer structure of ferromagnetic materials with complex interfaces has been found. The dependency graphs of the reflection coefficient from the frequency of the spin waves at different parameters of magnetic anisotropy inhomogeneity and constant value of the external magnetic field were obtained. Conclusions. It is shown that the frequency dependencies are periodic, points of full transmission and areas, full of reflection. Decreasing exchange parameter value in interface causes the increase of reflectance coefficient. Changing the material parameters we get the necessary intensity value of the reflection coefficient depending on the frequency at a constant value of the external magnetic field.

Ginzburg-Landau free energy for molecular fluids: Determination and coarse-graining

Using molecular simulation, we determine Ginzburg-Landau free energy functions for molecular fluids. To this aim, we extend the Expanded Wang-Landau method to calculate the partition functions, number distributions and Landau free energies for Ar,CO2 and H2O. We then parametrize a coarse-grained free energy function of the density order parameter and assess the performance of this free energy function on its ability to model the onset of criticality in these systems. The resulting parameters can be readily used in hybrid atomistic/continuum simulations that connect the microscopic and mesoscopic length scales.

Resource allocation under a strategic alliance: How a cooperative network with knowledge flow spurs co-evolution

This article explores how a cooperative network with knowledge flow spurs co-evolution under a strategic alliance. For this purpose, this article analyzes the principle of a strategic alliance’s cooperative network with knowledge flow based on four different types of resource allocation patterns. Further, it presents a theoretical model of co-evolution by using co-evolution game and Synergetics order parameters while simulating the core order parameter density distribution and vector field. The result shows that the cooperative network with knowledge flow under a strategic alliance features path mutation, preferences and spontaneous symmetry breaking. Relationship-oriented and knowledge-embedded resource allocation patterns maintain the stability of network co-evolution. Both the technological network and social relationship network coexist in the course of co-evolution of a cooperative network with knowledge flow under a strategic alliance. If external actions have not been achieved, the cooperative network may still be self-sufficient until the network reaches stability.

New density functional approach for solid-liquid-vapor transitions in pure materials.

A new phase field crystal (PFC) type theory is presented, which accounts for the full spectrum of solid-liquid-vapor phase transitions within the framework of a single density order parameter. Its equilibrium properties show the most quantitative features to date in PFC modeling of pure substances, and full consistency with thermodynamics in pressure-volume-temperature space is demonstrated. A method to control either the volume or the pressure of the system is also introduced. Nonequilibrium simulations show that 2- and 3-phase growth of solid, vapor, and liquid can be achieved, while our formalism also allows for a full range of pressure-induced transformations. This model opens up a new window for the study of pressure driven interactions of condensed phases with vapor, an experimentally relevant paradigm previously missing from phase field crystal theories.

The Intramolecular Pressure and the Extension of the Critical Point’s Influence Zone on the Order Parameter

The critical point affects the coexistence behavior of the vapor-liquid equilibrium densities. The length of the critical influence zone is under debate because for some properties, like shear viscosity, the extension is only a few degrees, while for others, such as the density order parameter, the critical influence zone covers up to hundreds of degrees below the critical temperature. Here we show that, for ethane, the experimental critical influence zone covers a wide zone of tens of degrees (below the critical temperature) down to a transition temperature, at which the apparent critical influence zone vanishes, and the transition temperature can be predicted through a pressure analysis of the coexisting bulk liquid phase, using a simple molecular potential. The liquid phases within the apparent critical influence zone show low densities, making them behave internally like their corresponding vapor phases. Therefore, Molecular Dynamics simulations reveal that the experimentally observed wide extension of the critical influence zone is the result of a vapor-like effect due to low bulk liquid phase densities.

Vanishing order-parameter critical fluctuations of an absorbing-state transition driven by long-range interactions

We study the critical behavior of the absorbing-state phase transition depicted by a contact process one-dimensional model system with power-law decaying interactions. The system dynamical processes include particle creation at a rate which decays with the distance from the nearest particle as $1/{r}^{\ensuremath{\alpha}}$. This model displays an absorbing-state phase transition with critical exponents varying continuously with the interaction exponent $\ensuremath{\alpha}$. Here, we provide a finite-size scaling analysis of the stationary order-parameter density, one of its moment ratio, its logarithmic derivative, and fluctuations. We also follow the short-time relaxation dynamic of these quantities to estimate their corresponding dynamical critical exponents. The estimated exponents are shown to be consistent with the hyperscaling relation. Further, we report an unconventional regime on which the critical order-parameter fluctuations vanish in the thermodynamic limit.

Bond orientational order in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization

There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases a complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is the most poorly understood. We argue that it is crucial for a better understanding of liquids to recognize that a liquid generally has the tendency to have a local structural order and its presence is intrinsic and universal to any liquid. Such structural ordering is a consequence of many-body correlations, more specifically, bond angle correlations, which we believe are crucial for the description of the liquid state. We show that this physical picture may naturally explain difficult unsolved problems associated with the liquid state, such as anomalies of water-type liquids (water, Si, Ge, ...), liquid-liquid transition, liquid-glass transition, crystallization and quasicrystal formation, in a unified manner. In other words, we need a new order parameter representing a low local free-energy configuration, which is a bond orientational order parameter in many cases, in addition to a density order parameter for the physical description of these phenomena. Here we review our two-order-parameter model of liquid and consider how transient local structural ordering is linked to all of the above-mentioned phenomena. The relationship between these phenomena is also discussed.

Optical Bragg, atomic Bragg and cavity QED detections of quantum phases and excitation spectra of ultracold atoms in bipartite and frustrated optical lattices

Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases and quantum phase transitions between these phases. However, so far, how to detect these quantum phases and phase transitions effectively remains an outstanding challenge. In this paper, we will develop a systematic and unified theory of using the optical Bragg scattering, atomic Bragg scattering or cavity QED to detect the ground state and the excitation spectrum of many quantum phases of interacting bosons loaded in bipartite and frustrated optical lattices. The physically measurable quantities of the three experiments are the light scattering cross sections, the atom scattered clouds and the cavity leaking photons respectively. We show that the two photon Raman transition processes in the three detection methods not only couple to the density order parameter, but also the valence bond order parameter due to the hopping of the bosons on the lattice. This valence bond order coupling is very sensitive to any superfluid order or any valence bond (VB) order in the quantum phases to be probed. These quantum phases include not only the well-known superfluid and Mott insulating phases, but also other important phases such as various kinds of charge density waves (CDW), valence bond solids (VBS), and CDW-VBS phases with both CDW and VBS orders unique to frustrated lattices, and also various kinds of supersolids. We analyze respectively the experimental conditions of the three detection methods to probe these various quantum phases and their corresponding excitation spectra. We also address the effects of a finite temperature and a harmonic trap. We contrast the three scattering methods with recent in situ measurements inside a harmonic trap and argue that the two kinds of measurements are complementary to each other. The combination of both kinds of detection methods could be used to match the combination of Scanning tunneling microscopy (STM), the Angle Resolved Photo Emission spectroscopy (ARPES) and neutron scattering in condensed matter systems, therefore achieve the putative goals of quantum simulations

Quantum phase transition in quarter-filled nanoclusters of manganite induced by element substitution at B site

In the present paper, we study the effect of element substitution for quarter-filled nanoclusters of perovskite manganite by introducing Jahn-Teller type of perturbation interaction to the double-exchange Hamiltonian. Using the unrestricted real-space Hartree-Fock approximation method we find that, the Jahn-Teller electron-phonon interaction plays the central role in producing the phase transition from ferromagnetic phase to CE type antiferromagnetic phase. Not only the Jahn-Teller interaction benefits antiferromagnetic correlation, it also increases the charge density order parameter. These theoretical results provide a guidance to predict the properties and modify the composition of particles of perovskite manganite under nano-scale.

Bond orientational ordering in a metastable supercooled liquid: a shadow of crystallizationand liquid–liquid transition

It is widely believed that a liquid state can be characterized by a single order parameter,density, and that a transition from a liquid to solid can be described by density ordering(translational ordering). For example, this type of theory has had great success indescribing the phase behaviour of hard spheres. However, there are some features thatcannot be captured by such theories. For example, hard spheres crystallize into either hcpor fcc structures, without a tendency of bcc ordering which is expected by theAlexander–McTague theory based on the Landau-type free energy of the density orderparameter. We also found hcp-like bond orientational ordering in a metastablesupercooled liquid, which promotes nucleation of hcp crystals. Furthermore, theoriesbased on the single order parameter cannot explain water-like thermodynamic andkinetic anomalies of a liquid and liquid–liquid transition in a single-componentliquid. Based on these facts, we argue that we need an additional order parameterto describe a liquid state. It is bond orientational order, which is induced bydense packing in hard spheres or by directional bonding in molecular and atomicliquids. Bond orientational order is intrinsically of local nature, unlike translationalorder which is of global nature. This feature plays a unique role in crystallizationand quasicrystal formation. We also reveal that bond orientational ordering isa cause of dynamic heterogeneity near a glass transition and is linked to slowdynamics. In relation to this, we note that, for describing the structuring of ahighly disordered liquid, we need a structural signature of low configurationalentropy, which is more general than bond orientational order. Finally, the water-likeanomaly and liquid–liquid transition can be explained by bond orientational orderingdue to hydrogen or covalent bonding and its cooperativity, respectively. So weargue that bond orientational ordering is a key to the physical understanding ofcrystallization, quasicrystallization, glass transition, water-like anomaly and liquid–liquidtransition. A unified description of these phenomena may be possible along thisline.

The escape transition of a polymer: A unique case of non-equivalence between statistical ensembles

A flexible polymer chain under good solvent conditions, end-grafted on a flat repulsive substrate surface and compressed by a piston of circular cross-section with radius L may undergo the so-called "escape transition" when the height of the piston D above the substrate and the chain length N are in a suitable range. In this transition, the chain conformation changes from a quasi-two-dimensional self-avoiding walk of "blobs" of diameter D to an inhomogeneous "flower" state, consisting of a "stem" (stretched string of blobs extending from the grafting site to the piston border) and a "crown" outside of the confining piston. The theory of this transition is developed using a Landau free-energy approach, based on a suitably defined (global) order parameter and taking also effects due to the finite chain length N into account. The parameters of the theory are determined in terms of known properties of limiting cases (unconfined mushroom, chain confined between infinite parallel walls). Due to the non-existence of a local order parameter density, the transition has very unconventional properties (negative compressibility in equilibrium, non-equivalence between statistical ensembles in the thermodynamic limit, etc.). The reasons for this very unusual behavior are discussed in detail. Using Molecular Dynamics (MD) simulation for a simple bead-spring model, with N in the range 50<or=N<or=300, a comprehensive study of both static and dynamic properties of the polymer chain was performed. Even though for the considered rather short chains the escape transition is still strongly rounded, the order parameter distribution does reveal the emerging transition clearly. Time autocorrelation functions of the order parameter and first passage times and their distribution indicate clearly the strong slowing down associated with the chain escape. The theory developed here is in good agreement with all these simulation results.

Surface superconducting states and paramagnetism in mesoscopic superconductors

In the framework of the Ginzburg-Landau equation, the temperature dependence of the upper critical field of small thin ringlike superconductors is studied. At equilibrium small parts of the phase diagram show paramagnetism for small hole sizes (larger than 15%). Their number and extension increase with the size of the hole. In these regions, only the inner part of the ring shows a positive magnetic moment. The order parameter density profile appears to change when crossing a first order transition line which separates different angular momentum values. We clarify the relationship between the localization of superconductivity nucleation and paramagnetism of these samples.

The ice/water interface: orientational order parameters for the basal, prism, {202̄1}, and {21̄1̄0} interfaces of ice Ih

Orientational order parameters for four crystallographically distinct ice/water interfaces are defined and measured in molecular dynamics computer simulations of the CF1 central force model of water. We find that all interfaces are broad, with consistently different orientational structures found among the four interfaces. We also define and measure a local order parameter in the interfaces related to oxygen–oxygen coordination number, and show that this measure of the interfacial width is extremely broad. Combining recent results for the translational order parameters, average density order parameters and diffusion coefficient order parameters, for this model of water, coupled with other simulations of rigid models of water, a clear picture of the structure of the ice/water interface emerges. This also reveals a possible explanation for the differential accumulation of certain solutes at the ice/water interface.

Local Relaxation Approach to the Non Fermi Liquid and Strongly Correlated Electronic States

In non Fermi liquid materials which lie close to a magnetic instability empirical analysis suggests a convenient set of independent variables for the description of experimental data to be given by the set of spontaneous fluctuations in the local magnetisation density. In this article an overview of such an analysis is given with a discussion of a microscopic background to motivate this step beyond the confines of homogeneous mean field theories. The basic postulate is to associate an explicit dynamical phase field with the magnetisation density order parameter.

Bond-order driven metallic stripes in the t– U– J model

We studied the stripe formation in the t– U– J model with the nearest neighbor antiferromagnetic spin correlation J and the onsite Coulomb repulsion U. The model was decoupled using the Hartree–Fock–Bogoliubov approximation in the real space. The resulting Bogoliubov–de-Gennes equation was then solved as the doping concentration is varied, with the d-wave pairing, nearest neighbor bond-order, local spin density, and charge density order parameters determined self-consistently. An antiphase metallic stripe with magnetic unit cell of 8 a at hole doping 1/8 was obtained when the next nearest hopping t ′ is allowed in this model. By comparing the results from with and without the bond-order parameter with each other, we conclude that the bond-centered metallic stripes are stabilized by the additional reduction in kinetic energy when the bond order is developed.

First- and second-order phase transitions in a driven lattice gas with nearest-neighbor exclusion

A lattice gas with infinite repulsion between particles separated by < or = 1 lattice spacing, and nearest-neighbor hopping dynamics, is subject to a drive favoring movement along one axis of the square lattice. The equilibrium (zero drive) transition to a phase with sublattice ordering, known to be continuous, shifts to lower density, and becomes discontinuous for large bias. In the ordered nonequilibrium steady state, both the particle and order-parameter densities are nonuniform, with a large fraction of the particles occupying a jammed strip oriented along the drive. The drive thus induces separation into high- and low-density regions in a system with purely repulsive interactions. Increasing the drive can provoke a transition to the ordered phase, and thereby, a sharp reduction in current.