Nature of crossover between ising-like and mean-field critical behavior in fluids and fluid mixtures

An Analysis of the Critical Region of Multiparameter Equations of State

In this work, two classes of defects with multiparameter equations of state are investigated. In the first, it is shown that the critical point provided by equation of state developers often does not exactly meet the criticality conditions based on the first two density derivatives of the pressure being zero at the critical point. Based on the more accurate locations of the critical points given in the first part, the scaling of the densities along the binodal and spinodal in the critical region are investigated, and we find that the vast majority of equations have reasonable behavior but a few do not.

Universality, Scaling, and Collapse in Supercritical Fluids

Supercritical fluid (SCF) is known to exhibit salient dynamic and thermodynamic crossovers and an inhomogeneous molecular distribution. However, the question as to what basic physics underlies these microscopic and macroscopic anomalies remains open. Here, using an order parameter extracted by machine learning, the fraction of gas-like (or liquid-like) molecules, we find simplicity and universality in SCF: First, all isotherms of a given fluid collapse onto a single master curve described by a scaling relation. The observed power law holds from the high-temperature and -pressure regime down to the critical point where it diverges. Second, phase diagrams of different compounds collapse onto their master curves by the same scaling exponent, thereby demonstrating a putative law of corresponding supercritical states in simple fluids. The reported results support a model of the SCF as a mixture of two interchangeable microstates, whose spatiotemporal dynamics gives rise to unique macroscopic properties.

Does shear viscosity relaxation control the dynamics of critical fluctuations in polystyrene-cyclohexane?

Between 20 and 90 MHz frequency-dependent shear viscosities of the polystyrene-cyclohexane mixture of critical composition have been measured at polymer molar weight Mw = 30,000. The viscosity data reveal dispersion, in conformity with relaxation characteristics in the non-critical background contributions to the ultrasonic attenuation, i.e., in the longitudinal viscosity of the critical system. The dispersion behavior is discussed with a view to its effect on the critical dynamics of the liquid near its consolute point. Attention is especially given to the relaxation rates of fluctuations of that system. The data as resulting from ultrasonic attenuation spectroscopy on the one hand and from quasi-elastic light scattering and viscosity measurements on the other hand differ near the critical temperature. It is concluded that likely an additional dispersion exists in the shear viscosity at frequencies below the presently available frequency range of measurement.

Critical behavior of nanoparticle-containing binary liquid mixtures

Simultaneous measurements of small-angle neutron scattering and dynamic light scattering have been performed on a binary mixture of partially miscible liquids, 2,6-dimethylpyridine and water. At critical composition the temperature dependence of the correlation length of fluctuations in composition is strongly affected by the addition of nanoparticles of a triblock copolymer polyethylene oxide-polypropylene oxide-polyethylene oxide. A crossover between Ising-type critical behavior and mean-field critical behavior is observed when the correlation length is equal to the size of the nanoparticles.

Large heat capacity anomaly near the consolute point of the binary mixture nitromethane and 3-pentanol

The large critical anomaly in the isobaric heat capacity C(p,x)(T) of the binary mixture nitromethane + 3-pentanol is measured using high-resolution adiabatic scanning calorimetry. The unique features of this technique provided an alternative approach to the study of the critical behavior of C(p,x)(T), providing further C(p,x)(T) related quantities from which valuable information could be extracted. Our data are in full agreement with the predictions of the Modern Theory of Critical Phenomena; specifically, 3D-Ising model values for the critical exponent α and the universal amplitude ratio values of the leading critical amplitudes, as well as for the first correction-to-scaling ones, provide the optimum fits to represent the experimental data. Evidence for the need of higher-order terms, i.e., first correction-to-scaling term, is given. The large value of the coefficient E for the linear temperature dependence of the background obtained is ascribed to a possible contribution of the regular linear background term, of a higher-order asymmetry term, and of the second correction-to-scaling term. Internal consistency of C(p,x)(T) and its related quantities is successfully checked.

Critical behavior on approaching a special critical point in a complex fluid

The critical behavior of osmotic susceptibility is investigated in the re-entrant complex mixture 1-propanol (P)+water (W)+potassium chloride (KCl) through light-scattering measurements. The measurements are performed on approaching a special critical point [i.e., the double critical point (DCP)] in this mixture, along the line of upper critical solution temperatures (T(U)'s), by varying t from the high temperature one-phase region. The light-scattering data analysis emphasizes the need for corrections to the asymptotic Ising behavior and yields very large magnitudes for the correction-to-scaling amplitudes A(1) and A(2), with the first-correction amplitude A(1) being negative, signifying a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the T(U) closest to the DCP, the effective susceptibility exponent gamma(eff) displays a nonmonotonic crossover from its nearly doubled three dimensional (3D)-Ising value toward its nearly double mean-field value with an increase in t. While for that far away from the DCP, it displays a nonmonotonic crossover from its single-limit Ising value toward a value slightly lower than its mean-field value of 1 with an increase in t. This feature of the effective susceptibility exponent is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values in the nonasymptotic high t region. The renormalized Ising regime extends over a larger t range for the sample (or T(U)) closest to the DCP when compared to that far away from it. The in-between T(U)'s display a trend toward shrinkage in the renormalized Ising regime as T(U) shifts away from the DCP. Nevertheless, the crossover to the mean-field behavior is completed only beyond t>10(-2) for the T(U)'s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques, while the observed unique trend in the crossover behavior is discussed in terms of the varying influence of the DCP on the critical behavior along the T(U) line. The crossover behavior for the T(U)'s is pronounced and more sharp compared to the T(L)'s (lower critical solution temperatures) [U. K. Pradeep, J. Chem. Phys. 129, 134506 (2008)] in this mixture, although there exists no difference in the growth of the mesoscale clusters in the lower and upper one-phase regions in this mixture. Our observations suggest the need to look at the crossover behavior probably from two perspectives, namely, the dielectric effect and the clustering effect. The effective susceptibility exponent as a function of the field variable t(UL), instead of the conventional variable t, displays a sharp nonmonotonic crossover from its asymptotic 3D-Ising value ( approximately 1.24) toward a value slightly lower than its nonasymptotic mean-field value of 1, as that observed in the t analysis for the T(U) far away from the influence of the DCP.

Master crossover functions for one-component fluids

By introducing three well-defined dimensionless numbers, we establish the link between the scale dilatation method able to estimate master (i.e., unique) singular behaviors of the one-component fluid subclass and the universal crossover functions recently estimated [Garrabos and Bervillier, Phys. Rev. E 74, 021113 (2006)] from the bounded results of the massive renormalization scheme applied to the Phi(d)(4)(n) model of scalar order parameter (n=1) and three dimensions (d=3), representative of the Ising-like universality class. The master (i.e., rescaled) crossover functions are then able to fit the singular behaviors of any one-component fluid without adjustable parameter, using only one critical energy scale factor, one critical length scale factor, and two dimensionless asymptotic scale factors, which characterize the fluid critical interaction cell at its liquid-gas critical point. An additional adjustable parameter accounts for quantum effects in light fluids at the critical temperature. The effective extension of the thermal field range along the critical isochore where the master crossover functions seems to be valid corresponds to a correlation length greater than three times the effective range of the microscopic short-range molecular interaction.

Two-parameter scaling of correlation functions near continuous phase transitions

We discuss the order parameter correlation function in the vicinity of continuous phase transitions using a two-parameter scaling form G(k)=kc(-2)g(kxi,k/kc), where k is the wave vector and xi is the correlation length, and the interaction-dependent nonuniversal momentum scale kc remains finite at the critical fixed point. The correlation function describes the entire critical regime and captures the classical to critical crossover. One-parameter scaling is recovered only in the limit k/kc-->0. We present an approximate calculation of g(x,y) for the Ising universality class using the functional renormalization group.

Ion-induced multiply reentrant liquid-liquid transitions and the nature of criticality in ethanol-water mixture

We report a quite unusual feature of four liquid-liquid reentrant transitions in ethanol (E)+water (W)+ammonium sulfate mixture by meticulous tuning of the ammonium sulfate concentration in a narrow range, as a function of temperature, at atmospheric pressure. Detailed exploration of the intricate phase behavior in terms of E/W sections shows that the range of triple reentrance shrinks with increasing E/W. The behavior of osmotic susceptibility is investigated by light scattering, near the critical point, in the one-phase region by varying the temperature at fixed concentration of the components, in a particular E/W section. The critical exponent of susceptibility (gamma) and correlation length (nu) are observed to have Fisher renormalized Ising values [Phys. Rev. 176, 237 (1968)], with gamma(r)=1.41 and nu(r)=0.718. The effective susceptibility exponent, gamma(eff), exhibits a sharp, nonmonotonic crossover from Ising to mean-field critical behavior, which is completed outside the critical regime. The amplitude of the correlation length, xi(o)(=21.2+/-0.4 A), deduced from light scattering experiment, is an order of magnitude larger than the typical values in usual aqueous electrolyte systems. This value of xi(o) is further verified from small-angle x-ray scattering (SAXS) experiments and found to be consistent. SAXS experiments on the critical sample reveal the presence of long-ranged intermolecular correlations, leading to supramolecular structuring, at a temperature far away from the critical point. These results convincingly demonstrate that the finite length scale arising due to the structuring competes with the diverging correlation length of critical concentration fluctuations, which influences the nonasymptotic critical behavior in this aqueous electrolyte system. The sulphate ions play a dominant role in both structuring and the complex phase behavior.

Critical behavior of 2,6-dimethylpyridine-water: Measurements of specific heat, dynamic light scattering, and shear viscosity

The specific heat C(p) at constant pressure, the shear viscosity eta(s), and the mutual diffusion coefficient D of the 2,6-dimethylpyridine-water mixture of critical composition have been measured in the homogeneous phase at various temperatures near the lower critical demixing temperature T(c). The amplitude of the fluctuation correlation length xi(0)=(0.198+/-0.004) nm has been derived from a combined evaluation of the eta(s) and D data. This value is in reasonable agreement with the one obtained from the amplitude A(+)=(0.26+/-0.01) J(g K) of the critical term in the specific heat, using the two-scale-factor universality relation. Within the limits of error the relaxation rate Gamma of order parameter fluctuations follows power law with the theoretical universal exponent and with the amplitude Gamma=(25+/-1)x10(9) s(-1). No indications of interferences of the critical fluctuations with other elementary chemical reactions have been found. A noteworthy result is the agreement of the background viscosity eta(b), resulting from the treatment of eta(s) and D data, with the viscosity eta(s)(nu=0) extrapolated from high-frequency viscosity data. The latter have been measured in the frequency range of 5-130 MHz using a novel shear impedance spectrometer.

Lattice model of equilibrium polymerization. V. Scattering properties and the width of the critical regime for phase separation

Dynamic clustering associated with self-assembly in many complex fluids can qualitatively alter the shape of phase boundaries and produce large changes in the scale of critical fluctuations that are difficult to comprehend within the existing framework of theories of critical phenomena for nonassociating fluids. In order to elucidate the scattering and critical properties of associating fluids, we consider several models of equilibrium polymerization that describe widely occurring types of associating fluids at equilibrium and that exhibit the well defined cluster geometry of linear polymer chains. Specifically, a Flory-Huggins-type lattice theory is used, in conjunction with the random phase approximation, to compute the correlation length amplitude xi(o) and the Ginzburg number Gi corresponding, respectively, to the scale of composition fluctuations and to a parameter characterizing the temperature range over which Ising critical behavior is exhibited. Our calculations indicate that upon increasing the interparticle association energy, the polymer chains become increasingly long in the vicinity of the critical point, leading naturally to a more asymmetric phase boundary. This increase in the average degree of polymerization implies, in turn, a larger xi(o) and a drastically reduced width of the critical region (as measured by Gi). We thus obtain insight into the common appearance of asymmetric phase boundaries in a wide range of "complex" fluids and into the observation of apparent mean field critical behavior even rather close to the critical point.

Methyl ethyl ketone+water+secondary butyl alcohol: A potential system for the exploration of a quadruple critical point

We report preliminary experiments on the ternary-liquid mixture, methyl ethyl ketone (MEK)+water (W)+secondary butyl alcohol (sBA)--a promising system for the realization of the quadruple critical point (QCP). The unusual tunnel-shaped phase diagram shown by this system is characterized and visualized by us in the form of a prismatic phase diagram. Light-scattering experiments reveal that (MEK+W+sBA) shows near three-dimensional-Ising type of critical behavior near the lower critical solution temperatures, with the susceptibility exponent (gamma) in the range of 1.217< or =gamma< or =1.246. The correlation length amplitudes (xio) and the critical exponent (nu) of the correlation length (xi) are in the ranges of 3.536< or =xio < or =4.611 A and 0.619< or =nu< or =0.633, respectively. An analysis in terms of the effective susceptibility exponent (gammaeff) shows that the critical behavior is of the Ising type for MEK concentrations in the ranges of 0.1000< or =X< or =0.1250 and X> or =0.3000. But, for the intermediate range of 0.1750< or =X<0.3000, the system shows a tendency towards mean-field type of critical behavior. The advantages of the system (MEK+W+sBA) over the system (3-methylpyridine+water+heavy water+potassium Iodide) for the realization of a QCP are outlined.

Critical behavior of the aqueous electrolytic system 3-methylpyridine+D2O+NaBr

The system 3-methylpyridine(3MP) + water(H2O)+NaBr has been the subject of an intense scientific debate since the work of Jacob et al. [Phys. Rev. E. 58, 2188 (1988)] and Anisimov et al. [Phys. Rev. Lett. 85, 2336 (2000)]. The crossover critical behavior of this system seemed to show remarkable sensitivity to the weight fraction (X) of the ionic impurity NaBr. In the range X< or =0.10 the system displayed Ising behavior and a pronounced crossover to mean-field behavior in the range 0.10< or =X< or =0.16. A complete mean-field behavior was observed at X=0.17, a result that was later attributed to the existence of long-living nonequilibrium states in this system [Kostko et al., Phys. Rev. E. 70, 026118 (2004)]. In this paper, we report the near-critical behavior of osmotic susceptibility in the isotopically related ternary system, 3MP+heavy water(D2O)+NaBr. Detailed light-scattering experiments performed at exactly the same NaBr concentrations as investigated by Jacob et al. reveal that the system 3MP + D2O + NaBr shows a simple Ising-type critical behavior with gamma approximately 1.24 and nu approximately 0.63 over the entire NaBr concentration range 0< or =X< or =0.1900. The crossover behavior is predominantly nonmonotonic and is completed well outside the critical domain. An analysis in terms of the effective susceptibility exponent (gammaeff) reveals that the crossover behavior is nonmonotonic for 0< or =X< or =0.1793 and tends to become monotonic for X>0.1793. The correlation length amplitude xio, has a value of approximately 2 A for 0.0250< or =X< or =0.1900, whereas for X=0, xio approximately 3.179 A. Since isotopic H-->D substitution is not expected to change the critical behavior of the system, our results support the recent results obtained by Kostko et al. [Phys. Rev. E. 70, 026118 (2004)] that 3MP + H2O + NaBr exhibits universal Ising-type critical behavior typical for other aqueous solutions.

Competition of mesoscales and crossover to theta-point tricriticality in near-critical polymer solutions

The approach to asymptotic critical behavior in polymer solutions is governed by a competition between the correlation length of critical fluctuations diverging at the critical point of phase separation and an additional mesoscopic length scale, the radius of gyration. In this paper we present a theory for crossover between two universal regimes: a regime with Ising (fluctuation-induced) asymptotic critical behavior, where the correlation length prevails, and a mean-field tricritical regime with theta-point behavior controlled by the mesoscopic polymer chain. The theory yields a universal scaled description of existing experimental phase-equilibria data and is in excellent agreement with our light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 2 x 10(5) up to 11.4 x 10(6). The experiments demonstrate unambiguously that crossover to theta-point tricriticality is controlled by a competition of the two mesoscales. The critical amplitudes deduced from our experiments depend on the polymer molecular weight as predicted by de Gennes [Phys. Lett. 26A, 313 (1968)]. Experimental evidence for the presence of logarithmic corrections to mean-field tricritical theta-point behavior in the molecular-weight dependence of the critical parameters is also presented.

Mean-field theory for inhomogeneous electrolytes

We calculate the free energy density for inhomogeneous electrolytes based on the mean-field Debye-Hückel theory. Derived are the contributions of (1) the differential term for the electrolyte density being slow varying in one direction and (2) the boundary term for an electrolyte confined to one side of a planar interface. These contributions are shown to cause an electrolyte depletion near the air-water interfaces, which makes the surface tension increase, to be significantly larger than those predicted by previous theories. Nonuniform electrolyte densities are also computed near the water-electrolyte and electrolyte-electrolyte interfaces. Finally we calculate the interaction of two uncharged macrospheres due to the electrolyte depletion.

Criticality in aqueous solutions of 3-methylpyridine and sodium bromide

We address a controversial issue regarding the nature of critical behavior in ternary electrolyte solutions of water, 3-methylpyridine, and sodium bromide. Earlier light-scattering studies showed an anomalous critical behavior in this system that was attributed to the formation of a microheterogeneous phase associated with ion-molecule clustering [M.A. Anisimov, J. Jacob, A. Kumar, V.A. Agayan, and J. V. Sengers, Phys. Rev. Lett. 85, 2336 (2000)]], while some other investigators subsequently found this system to exhibit ordinary Ising-like critical behavior. This contradiction forced us to revisit the problem and perform an accurate and comprehensive study of light scattering in this system paying attention to the achievement of thermodynamic equilibrium, hysteresis effects, aging, and prehistory of the samples, and a possible role of impurities. We show that properly aged, equilibrium samples of aqueous solutions of 3-methylpyridine with NaBr exhibit universal Ising-like critical behavior, typical for other aqueous solutions. No evidence for an equilibrium microheterogeneous phase was found. We have been able to reproduce anomalous behavior (similar to that reported initially) in a fast run on a freshly prepared sample. We attribute the observed anomalies to mesoscopic nonequilibrium aggregates, possibly associated with supramolecular restructuring in aqueous solutions. To support this conclusion we performed a study of aqueous solutions of 3-methylpyridine without NaBr and have found long-living nonequilibrium states in aqueous solutions of 3-methylpyridine.

Classical-to-critical crossovers from field theory

We extend our previous determinations of nonasymptotic critical behavior of Phys. Rev. B 32, 7209 (1985) and 35, 3585 (1987) to accurate expressions of the complete classical-to-critical crossover (in three-dimensional field theory) in terms of the temperaturelike scaling field (i.e., along the critical isochore) for (1) the correlation length, the susceptibility, and the specific heat in the homogeneous phase for the n-vector model (n=1 to 3) and (2) the spontaneous magnetization (coexistence curve), the susceptibility, and the specific heat in the inhomogeneous phase for the Ising model (n=1). The present calculations include the seventh-loop order of Murray and Nickel and closely account for the up-to-date estimates of universal asymptotic critical quantities (exponents and amplitude combinations) provided by Guida and Zinn-Justin [J. Phys. A 31, 8103 (1998)].

Competition of mesoscales and crossover to tricriticality in polymer solutions

We show that the approach to asymptotic fluctuation-induced critical behavior in polymer solutions is governed by a competition between a correlation length diverging at the critical point and an additional mesoscopic length-scale, the radius of gyration. Accurate light scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 200 000 up to 11.4x10(6) clearly demonstrate a crossover between two universal regimes: a regime with Ising asymptotic critical behavior, where the correlation length prevails, and a regime with tricritical theta-point behavior determined by a mesoscopic polymer-chain length.

Critical concentration fluctuations of the ionic binary mixture ethylammonium nitrate-n-octanol: an ultrasonic spectrometry study

Between 200 kHz and 130 MHz, the ultrasonic attenuation spectrum of the ionic ethylammonium nitrate--n-octanol mixture of critical composition has been measured at various reduced temperatures (1.5 x 10(-4)<or= t <or=5.7 x 10(-2)). Using static and dynamic light scattering data as well as viscosity and heat capacity data from the literature, the experimental spectra have been evaluated to yield the scaling function, with the background contribution to the spectra as the only adjustable parameter. Agreement, within the limits of experimental error, of the measured scaling function with that of the nonionic binary system ethanol--dodecane and with the theoretical predictions of the Bhattacharjee-Ferrell dynamic scaling model is found. The amplitude of the fluctuation correlation length xi(o) (=0.47 nm) and the amount of the coupling constant /g/ (=1.3) are rather high as compared to nonionic binary critical mixtures. The amplitude of the relaxation rate of order parameter fluctuations Gamma(o)(=2.6 x 10(8) s(-1)) exhibits an unusual small value, likely to the most part a reflection of the high viscosity and thus small diffusion coefficient of the ionic liquid.

Light scattering and crossover critical phenomena in polymer solutions

An accurate photon-correlation spectrometer capable of measuring scattered light at two fixed scattering angles simultaneously in the temperature range from 10 to 120 degrees C is described. For the detection of the correlation function of the scattered light both an original correlator (PhotoCor-SP) with a linear-time-scale channel spacing and an ALV GmbH correlator (Model ALV-5000) with a logarithmic-time-scale channel spacing are used. High-resolution static and dynamic light-scattering measurements near the critical point of a polystyrene solution were performed with this instrument. The static-intensity measurements reveal that the crossover from mean-field to Ising behavior occurs at a temperature at which the correlation length of the critical fluctuations becomes equal to the radius of gyration of the polymer molecule. We found that the wave-number dependence and the temperature dependence of the diffusion coefficient of the concentration fluctuations are not consistent with existing theory for critical dynamics in low-molecular-weight liquid mixtures.

Crossover parametric equation of state for Ising-like systems

We present a parametric equation for the thermodynamic properties in the critical region of three-dimensional Ising-like systems which include fluids and fluid mixtures. The equation of state incorporates a crossover from singular Ising behavior asymptotically close to the critical point to classical (mean-field) behavior further away from the critical point, characterized by two physical crossover parameters: a coupling constant related to the strength and range of molecular interactions and a "cutoff" wave number for the critical fluctuations. In the asymptotic Ising limit, the crossover equation reproduces the most recent theoretical estimates for the universal ratios of the leading and correction-to-scaling critical amplitudes. The equation has been tested by comparing it with recent experimental thermodynamic-property data for 3He near its vapor-liquid critical point.

Construction of an effective Hamiltonian for a three-dimensional Ising universality class

The asymptotic and preasymptotic critical behavior in fluids, mixtures, and uniaxial magnets is believed to be described by an effective straight phi(4) scalar field theory with suitable, nonuniversal, coupling constants. The critical parameters as well as the extent of crossovers and corrections to the leading critical behavior in physical systems, crucially depends on the choice of these couplings. Here we propose a new method for deriving the effective scalar field theory appropriate to a microscopic model in this universality class. Use is made of the hierarchical reference theory, which implements the basic ideas of Wilson momentum space renormalization group to microscopic Hamiltonians. The effective low-energy field theory is then analyzed by the minimal subtraction scheme of Schloms and Dohm. We discuss the application of this method to the three-dimensional Ising model and to the liquid-vapor phase transition. We make comparison with high-temperature expansion results and with experimental data for rare gas.

Crossover behavior in the isothermal susceptibility near the 3He critical point

We present high-resolution measurements of the isothermal susceptibility of pure 3He near the liquid-gas critical point. PVT measurements were performed in the single-phase region over the reduced temperature range 3 x 10(-5)<T/Tc-1<1.5 x 10(-1). The crossover behavior of the susceptibility along the critical isochore was analyzed using a field-theoretical renormalization-group calculation based on the phi4 model. A similar crossover analysis was performed on previously obtained Xe susceptibility measurements. A comparison of the rescaled susceptibility for 3He and Xe shows theoretically predicted universal crossover behavior.

Heat capacity behavior in the critical region of the ionic binary mixture ethylammonium nitrate-n-octanol

At temperatures between 30 degrees C and 58 degrees C we have recorded the heat capacity of the ionic ethylammonium nitrate-n-octanol mixture of critical composition and also of the constituents. Different samples of the binary mixture have been measured with its upper critical demixing temperature T(c) varying between 41.04 degrees C and 46.87 degrees C, depending on small traces of water within the liquid under test. Almost identical heat capacity profiles result if the data are displayed as a function of the temperature distance to the actual T(c) value. In the homogeneous phase the critical contribution exhibits power-law behavior with the critical exponent alpha=0.11 as theoretically predicted for nonionic liquids and in conformity with our understanding of the ionic criticality as being asymptotically Ising like. The noncritical background part of the heat capacity can be related to the heat capacities of the constituents using a simple mixture relation. In the two-phase regime a series of almost perfectly reproducible events is found which may be taken to indicate the existence of nonequilibrium intermediate states in the ethylammonium nitrate-n-octanol system.

Experimental evidence for crossover to mean-field tricritical behavior in a concentrated salt solution

We have discovered a mean-field multicritical point on the critical locus in an aqueous solution of 3-methylpyridine and sodium bromide. Light-scattering measurements indicate Ising-like asymptotic critical behavior at the lower salt concentrations. However, the temperature range of Ising critical behavior shrinks with increasing salt concentration and the critical behavior becomes mean-field-like at a concentration of about 17% mass fraction of NaBr. Emergence of a new characteristic length scale diverging at this point and a simultaneous pronounced increase in the background scattering suggests mean-field tricritical behavior associated with the formation of a microheterogeneous phase due to clustering of ions and molecules.

Crossover behavior in 3He and Xe near their liquid-vapor critical point

We present a detailed discussion of the crossover from mean-field to Ising critical behavior upon approach of the critical point, both for 3He and Xe. By combining different sets of experimental data, we are able to cover an unusually large temperature range on either side of the critical temperature T(c). Below T(c), we thus can make an accurate comparison with a recent calculation for the crossover of the coexistence curve. For the regime above T(c), an analysis of the compressibility demonstrates that the crossover regime in 3He is unexpectedly widened by a subtle interplay between quantum and critical fluctuations.

Criticality and crossover in accessible regimes

The near-critical behavior of (d = 3)-dimensional Ising-model ferromagnets or simple lattice gases with equivalent first, second, and third nearest-neighbor interactions is studied through Monte Carlo simulations using histogram reweighting techniques and comparisons with series expansions. By carefully analyzing numerical data from relatively small finite systems using scaling and extrapolation methods, it is demonstrated that one can reliably estimate critical exponents, critical temperatures, and universal amplitude ratios, thereby distinguishing convincingly between different "nearby" universality classes and revealing systematic crossover effects. This study is preparatory to extending similar techniques to study criticality in continuum fluid models lacking symmetries, with Coulomb interactions, etc.

Critical properties of the three-dimensional equivalent-neighbor model and crossover scaling in finite systems

Accurate numerical results are presented for the three-dimensional equivalent-neighbor model on a cubic lattice, for 12 different interaction ranges (coordination number between 18 and 250). These results allow the determination of the range dependences of the critical temperature and various critical amplitudes, which are compared to renormalization-group predictions. In addition, the analysis yields an estimate for the interaction range at which the leading corrections to scaling vanish for the spin-1 / 2 model, and confirms earlier conclusions that the leading Wegner correction must be negative for the three-dimensional (nearest-neighbor) Ising model. By complementing these results with Monte Carlo data for systems with coordination numbers as large as 52 514, the full finite-size crossover curves between classical and Ising-like behavior are obtained as a function of a generalized Ginzburg parameter. Also, the crossover function for the effective magnetic exponent is determined.