Nature of vapor-liquid asymmetry in fluid criticality

Thermodynamics and dynamics of coupled complex SYK models

It has been known that the large-qcomplex Sachdev-Ye-Kitaev (SYK) model falls under the same universality class as that of van der Waals (mean-field) and saturates the Maldacena-Shenker-Stanford (MSS) bound, both features shared by various black holes. This makes the SYK model a useful tool in probing the fundamental nature of quantum chaos and holographic duality. This work establishes the robustness of this shared universality class and chaotic properties for SYK-like models by extending to a system of coupled large-qcomplex SYK models of different orders. We provide a detailed derivation of thermodynamic properties, specifically the critical exponents for an observed phase transition, as well as dynamical properties, in particular the Lyapunov exponent, via the out-of-time correlator calculations. Our analysis reveals that, despite the introduction of an additional scaling parameter through interaction strength ratios, the system undergoes a continuous phase transition at low temperatures, similar to that of the single SYK model. The critical exponents align with the Landau-Ginzburg (mean-field) universality class, shared with van der Waals gases and various AdS black holes. Furthermore, we demonstrate that the coupled SYK system remains maximally chaotic in the large-qlimit at low temperatures, adhering to the MSS bound, a feature consistent with the single SYK model. These findings establish robustness and open avenues for broader inquiries into the universality and chaos in complex quantum systems. We provide a detailed outlook for future work by considering the 'very' low-temperature regime, where we discuss relations with the Hawking-Page phase transition observed in the holographic dual black holes. We present preliminary calculations and discuss the possible follow-ups that might be taken to make the connection robust.

Thermodynamic modeling of fluid polyamorphism in hydrogen at extreme conditions

Fluid polyamorphism, the existence of multiple amorphous fluid states in a single-component system, has been observed or predicted in a variety of substances. A remarkable example of this phenomenon is the fluid–fluid phase transition (FFPT) in high-pressure hydrogen between insulating and conducting high-density fluids. This transition is induced by the reversible dimerization/dissociation of the molecular and atomistic states of hydrogen. In this work, we present the first attempt to thermodynamically model the FFPT in hydrogen at extreme conditions. Our predictions for the phase coexistence and the reaction equilibrium of the two alternative forms of fluid hydrogen are based on experimental data and supported by the results of simulations. Remarkably, we find that the law of corresponding states can be utilized to construct a unified equation of state combining the available computational results for different models of hydrogen and the experimental data.

Liquid-vapor rectilinear diameter revisited

In the modern theory of critical phenomena, the liquid-vapor density diameter in simple fluids is generally expected to deviate from a rectilinear law approaching the critical point. However, by performing precise scannerlike optical measurements of the position of the SF_{6} liquid-vapor meniscus, in an approach much closer to criticality in temperature and density than earlier measurements, no deviation from a rectilinear diameter can be detected. The observed meniscus position from far (10K) to extremely close (1mK) to the critical temperature is analyzed using recent theoretical models to predict the complete scaling consequences of a fluid asymmetry. The temperature dependence of the meniscus position appears consistent with the law of rectilinear diameter. The apparent absence of the critical hook in SF_{6} therefore seemingly rules out the need for the pressure scaling field contribution in the complete scaling theoretical framework in this SF_{6} analysis. More generally, this work suggests a way to clarify the experimental ambiguities in the simple fluids for the near-critical singularities in the density diameter.

Compressible cell gas models for asymmetric fluid criticality

We thoroughly describe a class of models recently presented by Fisher and coworkers [Phys. Rev. Lett. 116, 040601 (2016)]PRLTAO0031-900710.1103/PhysRevLett.116.040601. The crucial feature of such models, termed compressible cell gases (CCGs), is that the individual cell volumes of a lattice gas are allowed to fluctuate. They are studied via the seldom-used (μ, p, T) ensemble, which leads to their exact mapping onto the Ising model. Remarkably, CCGs obey complete scaling, a formulation for the thermodynamic behavior of fluids near the gas-liquid critical point that accommodates features inherent to the asymmetric nature of this phase transition like the Yang-Yang (YY) and singular coexistence-curve diameter anomalies. The CCG_{0} models generated when volumes vary freely reveal local free volume fluctuations as the origin of these phenomena. Local energy-volume coupling is found to be another relevant microscopic factor. Furthermore, the CCG class is greatly extended by using the decoration transformation, with an interesting example being the Sastry-Debenedetti-Sciortino-Stanley model for hydrogen bonding in low-temperature water. The magnitude of anomalies is characterized by a single parameter, the YY ratio, which for the models so far considered here ranges from -∞ to 1/2.

Soluble Model Fluids with Complete Scaling and Yang-Yang Features

Yang-Yang (YY) and singular diameter critical anomalies arise in exactly soluble compressible cell gas (CCG) models that obey complete scaling with pressure mixing. Thus, on the critical isochore ρ=ρ(c), C(μ)≔-Td(2)μ/dT(2) diverges as |t|^(-α) when t∝T-T(c)→0^(-) while ρ(d)-ρ(c)∼|t|^(2β) where ρ(d)(T)=1/2[ρ(liq)+ρ(gas)]. When the discrete local CCG cell volumes fluctuate freely, the YY ratio R(μ)=C(μ)/C(V) may take any value -∞<R(μ)<1/2 but "anticorrelated" free volumes are needed for R(μ)>0. More general decorated CCGs, including "hydrogen bonding" water models, illuminate energy-volume coupling as relevant to R(μ).

Communication: Analytic continuation of the virial series through the critical point using parametric approximants

The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.

The Wide-Range Method to Construct the Entire Coexistence Liquid-Gas Curve and to Determine the Critical Parameters of Metals

A method to find the liquid-gas critical parameters of metallic elements is offered. It takes into account a nonanalytic behavior in the critical point vicinity and the Clapeyron-Clausius asymptotic behavior at low temperatures. The present approach provides good agreement with experimental data for a wide wealth of non-metallic substances and mercury and alkali metals, where the critical parameters and binodals are known from the measurements. We have also found the critical parameters and binodals for Al, Cu, Fe, and Zr, for which corresponding measurements are yet to be obtained.

Liquid nanodroplet formation through phase explosion mechanism in laser-irradiated metal targets

Some quantitative aspects of laser-irradiated pure metals, while approaching phase explosion, are still not completely understood. Here, we develop a model that describes the main quantities regulating the liquid-vapor explosive phase transition and the expulsion of liquid nanodroplets that, by solidifying, give rise to nanoparticle formation. The model combines both a thermodynamics description of the explosive phase change and a Monte Carlo simulation of the randomly generated critical vapor bubbles. The calculation is performed on a set of seven metals (Al, Fe, Co, Ni, Cu, Ag, and Au) which are frequently used in pulsed laser ablation experiments. Our final predictions about the size distribution of the liquid nanodroplets and the number ratio of liquid/vapor ejected atoms are compared, whenever possible, with available molecular dynamics simulations and experimental data.

Improved renormalization group theory for critical asymmetry of fluids

We develop an improved renormalization group (RG) approach incorporating the critical vapor-liquid equilibrium asymmetry. In order to treat the critical asymmetry of vapor-liquid equilibrium, the integral measure is introduced in the Landau-Ginzbug partition function to achieve a crossover between the local order parameter in Ising model and the density of fluid systems. In the implementation of the improved RG approach, we relate the integral measure with the inhomogeneous density distribution of a fluid system and combine the developed method with SAFT-VR (statistical associating fluid theory of variable range) equation of state. The method is applied to various fluid systems including square-well fluid, square-well dimer fluid and real fluids such as methane (CH4), ethane (C2H6), trifluorotrichloroethane (C2F3Cl3), and sulfur hexafluoride (SF6). The descriptions of vapor-liquid equilibria provided by the developed method are in excellent agreement with simulation and experimental data. Furthermore, the improved method predicts accurate and qualitatively correct behavior of coexistence diameter near the critical point and produces the non-classical 3D Ising criticality.

Asymmetric criticality of the osmotic compressibility in binary mixtures

Heat capacities in the critical and the non-critical regions for {benzonitrile + tridecane} and {benzonitrile + pentadecane}, and light scattering for {benzonitrile + undecane}, {benzonitrile + dodecane}, {benzonitrile + tridecane}, {benzonitrile + tetradecane}, {benzonitrile + pentadecane}, and {benzonitrile + hexadecane} in the critical two-phase region were measured. Light scattering measurements confirmed the existence of the asymmetry for the osmotic compressibility while no such asymmetry was observed for the correlation length. An analysis of the osmotic compressibility asymmetry suggested the dominance of the singular term |ΔT[circumflex]|(β), which supports the complete scaling theory. The consistency of the complete scaling theory in descriptions of different asymmetry behaviors was also discussed. Moreover, it was found that the contribution of the heat capacity-related term is also important in describing the asymmetry of the osmotic compressibility as it was observed in studies of the diameters of the coexistence curves.

Critical asymmetry in renormalization group theory for fluids

The renormalization-group (RG) approaches for fluids are employed to investigate critical asymmetry of vapour-liquid equilibrium (VLE) of fluids. Three different approaches based on RG theory for fluids are reviewed and compared. RG approaches are applied to various fluid systems: hard-core square-well fluids of variable ranges, hard-core Yukawa fluids, and square-well dimer fluids and modelling VLE of n-alkane molecules. Phase diagrams of simple model fluids and alkanes described by RG approaches are analyzed to assess the capability of describing the VLE critical asymmetry which is suggested in complete scaling theory. Results of thermodynamic properties obtained by RG theory for fluids agree with the simulation and experimental data. Coexistence diameters, which are smaller than the critical densities, are found in the RG descriptions of critical asymmetries of several fluids. Our calculation and analysis show that the approach coupling local free energy with White's RG iteration which aims to incorporate density fluctuations into free energy is not adequate for VLE critical asymmetry due to the inadequate order parameter and the local free energy functional used in the partition function.

Global asymmetry of fluids and local singularity in the diameter of the coexistence curve

By combining a measurable vapor-liquid coexistence curve and the extended van der Waals-type of equation of state (EOS) with the additional temperature-dependent coefficient, the phenomenological model of global fluid asymmetry has been developed separately for both coexisting bulk phases in the entire range of subcritical states. It is shown, in particular, that the adequate description of a liquid branch and its near-critical vicinity in terms of appropriate critical exponents and amplitudes connected by the two-scale-factor universal interrelations can be achieved. The asymmetric influence of heterophase fluctuations on the criticality of gaseous states is demonstrated. It is inherently similar to the well-known Fisher's droplet model, which corresponds to the scaling EOS too. The principle of corresponding isotherms has been formulated without any adjustable parameters. An attempt to avoid the use of a locally singular coexistence-curve diameter is proposed in the framework of two alternative models. The accurate vapor-liquid data for two fluid metals, Rb and Cs, as well as two molecular fluids, C(2)H(6) and CO(2), are reanalyzed by the above models to confirm the presumed opportunity.

Phase diagram and universality of the Lennard-Jones gas-liquid system

The gas-liquid phase transition of the three-dimensional Lennard-Jones particles system is studied by molecular dynamics simulations. The gas and liquid densities in the coexisting state are determined with high accuracy. The critical point is determined by the block density analysis of the Binder parameter with the aid of the law of rectilinear diameter. From the critical behavior of the gas-liquid coexisting density, the critical exponent of the order parameter is estimated to be β = 0.3285(7). Surface tension is estimated from interface broadening behavior due to capillary waves. From the critical behavior of the surface tension, the critical exponent of the correlation length is estimated to be ν = 0.63(4). The obtained values of β and ν are consistent with those of the Ising universality class.

Simulation of static critical phenomena in nonideal fluids with the lattice Boltzmann method

A fluctuating nonideal fluid at its critical point is simulated with the lattice Boltzmann method. It is demonstrated that the method, employing a Ginzburg-Landau free energy functional, correctly reproduces the static critical behavior associated with the Ising universality class. A finite-size scaling analysis is applied to determine the critical exponents related to the order parameter, compressibility and specific heat. A particular focus is put on finite-size effects and issues related to the global conservation of the order parameter.

Comparison of complete scaling and a field-theoretic treatment of asymmetric fluid criticality

We investigate the connection between the theory of complete scaling and a field-theoretic (FT) treatment of asymmetric fluid criticality. To facilitate the comparison, we develop an equation of state from a simplified form of the complete scaling transformations and systematically compare this equation of state with the equation of state generated by a FT treatment of an asymmetric Landau-Ginzburg-Wilson Hamiltonian. We find, with care in interpretation, that these two approaches may be read as equivalent up to terms involving an independent higher-order asymmetric correction-to-scaling exponent.

Critical behavior of the dielectric constant in asymmetric fluids

By applying a thermodynamic theory that incorporates the concept of complete scaling, we derive the asymptotic temperature dependence of the critical behavior of the dielectric constant above the critical temperature along the critical isochore and below the critical temperature along the coexistence curve. The amplitudes of the singular terms in the temperature expansions are related to the changes of the critical temperature and the critical chemical potential upon the introduction of an electric field. The results of the thermodynamic theory are then compared with the critical behavior implied by the classical Clausius-Mossotti approximation. The Clausius-Mossotti approximation fails to account for any singular temperature dependence of the dielectric constant above the critical temperature. Below the critical temperature it produces an apparent asymmetric critical behavior with singular terms similar to those implied by the thermodynamic theory, but with significantly different coefficients. We conclude that the Clausius-Mossotti approximation only can account for the observed asymptotic critical behavior of the dielectric constant when the dependence of the critical temperature on the electric field is negligibly small.

When depletion goes critical

Depletion interactions in correlated fluids are investigated both theoretically and experimentally. A formally exact derivation of a general expression for depletion interactions is presented and then specialized to the case of critical correlations in the depletant by employing a long wavelength approximate analysis. A scaling expression is obtained in the critical region, suggesting a close connection to the critical Casimir effect. As a result we are able to compute the full scaling function of the critical Casimir effect in terms of the known scaling form of the depletant equation of state. These predictions are experimentally tested in a colloidal suspension with a micellar solution as depletion agent. Colloids are seen to aggregate reversibly when the micellar concentration exceeds a temperature dependent value which becomes remarkably small as the temperature approaches the lower consolution point of the micellar suspension. Continuity between the standard depletion picture at low temperature and the Casimir effect in the critical region is demonstrated by identifying several approximate scaling laws which compare favorably with the theoretical analysis. The transition line is seen to lie close to the curve of maximum susceptibility of the depletant. A model, analyzed within mean field approximation, is shown to reproduce the main qualitative features of the phenomenon.

Asymmetric criticality in weakly compressible liquid mixtures

The thermodynamics of asymmetric liquid-liquid criticality is updated by incorporating pressure effects into the complete-scaling formulation earlier developed for incompressible liquid mixtures [C. A. Cerdeirina et al., Chem. Phys. Lett. 424, 414 (2006); J. T. Wang et al., Phys. Rev. E 77, 031127 (2008)]. Specifically, we show that pressure mixing enters into weakly compressible liquid mixtures as a consequence of the pressure dependence of the critical parameters. The theory is used to analyze experimental coexistence-curve data in the mole fraction-temperature, density-temperature, and partial density-temperature planes for a large number of binary liquid mixtures. It is shown how the asymmetry coefficients in the scaling fields are related to the difference in molecular volumes of the two liquid components. The work resolves the question of the so-called "best order parameter" discussed in the literature during the past decades.

Complete scaling for inhomogeneous fluids

"Complete scaling," which maps asymmetric fluid criticality onto the symmetric Ising model, is extended to spatially inhomogeneous fluids. This extension enables us to obtain a fluctuation-modified asymmetric interfacial density profile, which incorporates leading effects from the asymmetry of fluid phase coexistence and the asymmetry of the correlation length. The derived asymmetric interfacial profile is used to calculate Tolman's length, the diverging coefficient of the curvature correction to the surface tension. The amplitude of the divergent Tolman length is found to depend on the asymmetry of the correlation length.

Dielectric constant of fluids and fluid mixtures at criticality

The behavior of the dielectric constant epsilon of pure fluids and binary mixtures near liquid-gas and liquid-liquid critical points is studied within the concept of complete scaling of asymmetric fluid-fluid criticality. While mixing of the electric field into the scaling fields plays a role, pressure mixing is crucial as the asymptotic behavior of the coexistence-curve diameter in the epsilon-T plane is concerned. Specifically, it is found that the diameters, characterized by a |T-Tc|1-alpha singularity in the previous scaling formulation [J. V. Sengers, D. Bedeaux, P. Mazur, and S. C. Greer, Physica A 104, 573 (1980)], gain a more dominant |T-Tc|2beta term, whose existence is shown to be supported by literature experimental data. The widely known |T-Tc|1-alpha singularity of epsilon along the critical isopleth in the one-phase region is found to provide information on the effect of electric fields on the liquid-liquid critical temperature: from experimental data it is inferred that Tc usually decreases as the magnitude of the electric field is enhanced. Furthermore, the behavior of mixtures along an isothermal path of approach to criticality is also analyzed: theory explains why the observed anomalies are remarkably higher than those associated to the usual isobaric path.