Liquid-liquid critical point: an analytical approach

Theoretical simulations and experimental studies have showed that many systems (like liquid metals) can exhibit two phase transitions: gas-liquid and liquid-liquid. Consequently the fluid phase of these systems presents two critical points, namely the usual gas-liquid (G-L) critical point and the liquid-liquid critical point that results from a phase transition between two liquids of different densities: a low density liquid (LDL) and a high density liquid (HDL). The van der Waals theory for simple fluids [Phys. Rev. E 50, 2913 (1994)] is based on taking a system with purely repulsive forces as a reference, is able to describe two stable first-order phase transitions between fluids of different densities. The particles in our system interact via a total pair potential, which splits into a repulsive V_R and a density-dependent attractive V_A part.     

A semiclassical approximation for matrix elements involving non-orthogonal bound states

We analyse the phase diagram of a lattice gas model with both condenseation and order-disorder phase transitions, when the system is confined between two walls. The gas-liquid transition is shifted into the, so called, capillary condensation. The crystallization, both from the gas and from the liquid, is also shifted from the bulk values, but the ordered structure is frustrated or enhanced depending on its commensuration with the walls separation, H. This produces a strong oscillatory dependence of the phase diagram with H.     

Study of the solid-liquid-vapour phase equilibria of flexible chain molecules using Wertheim's thermodynamic perturbation theory

The phase diagram of flexible molecules formed by freely-jointed tangent spheres is studied using the first-order thermodynamic perturbation theory of Wertheim for both fluid and solid phases. A mean-field term is added to the free energy of the fluid and solid phase in order to account for attractive dispersion forces. The approach is used to determine the global (solid-liquid-vapour) phase diagrams and triple points of chain molecules of increasing chain length. It is found that the triple point temperature is not affected strongly by the length of the chain, whereas the gas-liquid critical temperature increases dramatically. The asymptotic limits of the phase diagram for infinitely long chains are discussed. The reduced critical temperature of infinitely long chains as given by the mean-field theory is 2/3, and the reduced triple point temperature is 0.048 56, so that an asymptotic value of T _t/T _c = 0.07284 for the ratio of the triple to critical point temperatures is obtained. This indicates that fully-flexible tangent chains present an enormous liquid range. The proposed theory, while being extremely simple, provides a useful insight into the phase behaviour of chain molecules, showing the existence of finite asymptotic limits for the triple and critical point temperatures. However, since n-alkanes present an asymptotic limit of about T _t/T _c, = 0.40, the agreement With experiment is not quantitative. This suggests that fully flexible models may not be appropriate to model the solid phases of real chain molecules.     

Floating liquid phase in sedimenting colloid-polymer mixtures

Density functional theory and computer simulation are used to investigate sedimentation equilibria of colloid-polymer mixtures within the Asakura-Oosawa-Vrij model of hard sphere colloids and ideal polymers. When the ratio of buoyant masses of the two species is comparable to the ratio of differences in density of the coexisting bulk (colloid) gas and liquid phases, a stable "floating liquid" phase is found, i.e., a thin layer of liquid sandwiched between upper and lower gas phases. The full phase diagram of the mixture under gravity shows coexistence of this floating liquid phase with a single gas phase or a phase involving liquid-gas equilibrium; the phase coexistence lines meet at a triple point. This scenario remains valid for general asymmetric binary mixtures undergoing bulk phase separation.     

Disappearance of the gas-liquid phase transition for highly charged colloids

We calculate the full phase diagram of spherical charged colloidal particles using Monte Carlo free energy calculations. The system is described using the primitive model, consisting of explicit hard-sphere colloids and point counterions in a uniform dielectric continuum. We show that the gas-liquid critical point becomes metastable with respect to a gas-solid phase separation at colloid charges Q > or =20 times the counterion charge. Approximate free energy calculations with only one and four particles in the fluid and solid phases, respectively, are used to determine the critical line for highly charged colloids up to Q=2000. We propose the scaling law T*(c) approximately Q(1/2) for this critical temperature.     

Hydrodynamic model for electron-hole droplets

The hydrodynamic equations of change are combined with the density functional formalism. This provides a model for critical and stable electron hole droplets which is applicable throughout the phase diagram.     

Simulation of phase boundaries using constrained cell models

Despite impressive advances, precise simulation of fluid-fluid and fluid-solid phase transitions still remains a challenging task. The present work focuses on the determination of the phase diagram of a system of particles that interact through a pair potential, ?(r), which is of the form ?(r)?=?4?[(σ/r)(2n)?-?(σ/r)(n)] with n?=?12. The vapor-liquid phase diagram of this model is established from constant-pressure simulations and flat-histogram techniques. The properties of the solid phase are obtained from constant-pressure simulations using constrained cell models. In the constrained cell model, the simulation volume is divided into Wigner-Seitz cells and each particle is confined to moving in a single cell. The constrained cell model is a limiting case of a more general cell model which is constructed by adding a homogeneous external field that controls the relative stability of the fluid and the solid phase. Fluid-solid coexistence at a reduced temperature of 2 is established from constant-pressure simulations of the generalized cell model. The previous fluid-solid coexistence point is used as a reference point in the determination of the fluid-solid phase boundary through a thermodynamic integration type of technique based on histogram reweighting. Since the attractive interaction is of short range, the vapor-liquid transition is metastable against crystallization. In the present work, the phase diagram of the corresponding constrained cell model is also determined. The latter is found to contain a stable vapor-liquid critical point and a triple point.     

零净液流量两相流持液率与阻力特性研究

分别以牛顿流体和非牛顿流体为液相，研究了垂直管中零净液流量气液两相流的流动特性。提出了零净液流量气液两相流动模型，应用这一模型计算了零净液流量气液两相流的持液率和压力降，模型计算结果与试验结果相符。研究结果表明，零净液流量气液两相流与常规气液两相流相比具有特殊性，表现为其持液率仅由质量平衡方程控制，其摩擦阻力压力降为负值。     

Bimodality and Coulomb effects with a canonical thermodynamic model

The effect of the Coulomb interaction on the phase diagram of finite nuclei is studied within the Canonical Thermodynamic Model. If Coulomb effects are artificially switched off, this model shows a phenomenology consistent with the liquid–gas phase transition. The inclusion of Coulomb does not significantly affect the phase diagram but it drastically modifies the nature and order parameter of the transition. A clear understanding of the phenomenon can be achieved looking at the distribution of the largest fragment produced in each fragmentation event. Possible connections with experimental observations are outlined.     

Competition between Kondo and RKKY correlations in the presence of strong randomness

We propose that competition between Kondo and magnetic correlations results in a novel universality class for heavy fermion quantum criticality in the presence of strong randomness. Starting from an Anderson lattice model with disorder, we derive an effective local field theory in the dynamical mean-field theory approximation, where randomness is introduced into both hybridization and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. Performing the saddle-point analysis in the U(1) slave-boson representation, we reveal its phase diagram which shows a quantum phase transition from a spin liquid state to a local Fermi liquid phase. In contrast with the clean limit case of the Anderson lattice model, the effective hybridization given by holon condensation turns out to vanish, resulting from the zero mean value of the hybridization coupling constant. However, we show that the holon density becomes finite when the variance of the hybridization is sufficiently larger than that of the RKKY coupling, giving rise to the Kondo effect. On the other hand, when the variance of the hybridization becomes smaller than that of the RKKY coupling, the Kondo effect disappears, resulting in a fully symmetric paramagnetic state, adiabatically connected to the spin liquid state of the disordered Heisenberg model. We investigate the quantum critical point beyond the mean-field approximation. Introducing quantum corrections fully self-consistently in the non-crossing approximation, we prove that the local charge susceptibility has exactly the same critical exponent as the local spin susceptibility, suggesting an enhanced symmetry at the local quantum critical point. This leads us to propose novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau-Ginzburg-Wilson paradigm. The Landau-Ginzburg-Wilson forbidden duality serves the mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.     

Phase diagram of silicon from atomistic simulations

In this Letter we present a calculation of the temperature-pressure phase diagram of Si in a range of pressures covering from -5 to 20 GPa and temperatures up to the melting point. The phase boundaries and triple points between the diamond, liquid, beta-Sn, and Si34 clathrate phases are reported. We have employed efficient simulation techniques to calculate free energies and to numerically integrate the Clausius-Clapeyron equation, combined with a tight-binding model capable of an accuracy comparable to that of first-principles methods. The resulting phase diagram agrees well with the available experimental data.     

Phase diagram of patchy colloids: towards empty liquids

We report theoretical and numerical evaluations of the phase diagram for patchy colloidal particles of new generation. We show that the reduction of the number of bonded nearest neighbors offers the possibility of generating liquid states (i.e., states with temperature T lower than the liquid-gas critical temperature) with a vanishing occupied packing fraction (phi), a case which can not be realized with spherically interacting particles. Theoretical results suggest that such reduction is accompanied by an increase of the region of stability of the liquid phase in the (T-phi) plane, possibly favoring the establishment of homogeneous disordered materials at small phi, i.e., stable equilibrium gels.     

Phase transitions in the antiferromagnetic ising model on a square lattice with next-nearest-neighbor interactions

The phase transitions in the two-dimensional Ising model on a square lattice are studied using a replica algorithm, the Monte Carlo method, and histogram analysis with allowance for the next-nearest-neighbor interactions in the range 0.1 ≤ r < 1.0. A phase diagram is constructed for the dependence of the critical temperature on the next-nearest-neighbor interaction. A second-order phase transition is detected in this range and the model under study.     

Nematic and chiral order for planar spins on a triangular lattice

We propose a variant of the antiferromagnetic XY model which includes a biquadratic (J2) as well as the quadratic (J1) interaction on the triangular lattice. The phase diagram for large J2/J1 exhibits a phase with coexisting quasi-long-range nematic, and long-ranged vector spin chirality orders in the absence of magnetic order, which qualifies our model as the first instance of a classical spin model that exhibits a vector chiral spin liquid phase. The interplay of nematic and spin chirality orders is discussed. A variety of critical properties are derived by means of Monte Carlo simulation.     

On the theory of vapor — Liquid — Crystal phase transitions

An approach is discussed which allows one to describe within the framework of the single model the aggregative states of a system of atoms obeying the Fermi statistics. A phase diagram is obtained containing both the critical point where the distinctions between the liquid and vapor vanish and the triple point where the liquid, vapor, and crystal are in equilibrium.     

The Equation of State and Phase Structure in A Model with Dynamical Spontaneous Symmetry Breaking at Finite Temperature and Density

Based on the Lurie model,a convenient scheme is constructed for calculating the equation of state approximately.The parametric equaion of state is given in the Lurie model.The phase diagram of the model shows the existence of critical point separating first order from second order chiral phase transition.The careful analysis of isotherms of pressure versus net baryon number density suggests the existence of overheat and overcool metastable state and the coexistence of broken phase and normal phase.     

Phase diagram and phase transitions of the adsorbate system S/Ru(0001): a Monte Carlo study of a lattice gas model

We investigate the phase diagram and the critical properties of the adsorbate system sulphur/ruthenium(0001) in the coverage region 0 < Θ < 1/3 using Monte Carlo simulations of a lattice gas model on a triangular lattice. From experiments it is known that for low coverages an island phase appears in the phase diagram of this system at low temperatures. To capture this feature we include in our lattice gas model a weak third neighbour attraction in addition to the repulsive first and second neighbour forces. The phase diagram obtained from simulations of this model is in very good agreement with the experimental phase diagram. The critical properties of the lattice gas model are found to be compatible with the results of experiments on the system sulphur/ruthenium(0001). Finer details of the phase diagram, e. g. the location of tricritical points, which may be difficult to assess experimentally will also be discussed.     

Possible exciton bose liquid in a hard-core boson ring model

We present a quantum Monte?Carlo study of a hard-core boson model with ring-only exchanges on a square lattice, where a K1 term acts on 1×1 plaquettes and a K2 term acts on 1×2 and 2×1 plaquettes. At half-filling, the phase diagram reveals charge density wave for small K2, valence bond solid for intermediate K2, and possibly for large K2 the novel exciton Bose liquid (EBL) phase first proposed by Paramekanti et?al [Phys. Rev. B 66, 054526 (2002)10.1103/PhysRevB.66.054526]. Away from half-filling, the EBL phase is present already for intermediate K2 and remains stable for a range of densities below 1/2 before phase separation sets in at lower densities.     

The Critical Properties of One—Dimensional Extended Hubbard Model

In the framework of nonperturbative quantum field theory,the critical phenomena of one-dimensional extended Hubbard model (EHM) at half-filling are discussed from weak to intermediate interactions.After the EHM being mapped into two decoupled sine-Gordon models,the ground state phase diagram of the system is derived in an explicit way.It is confirmed that the coexisting phases appear in different interaction regimes which cannot be found by conventional theoretical methods.The diagram shows that there are seven different phase regions in the ground state,which seems not to be the same as previous discussions,especially the boundary between the phase separation and condensed phase regions.The phase transition properties of the model between various phase regions are studied in detail.