Local order parameter near the critical point: A Monte Carlo study

The probability distribution of the local magnetization in a Heisenberg ferromagnet has been investigated near the critical temperature. The distribution function depends strongly upon the number of atoms generating the local field. A cusp-like critical broadening is observed with different behavior above and below the critical temperature.     

Dynamics of clusters near a critical point,central peak and EPR spectra

Our recently developed cluster theory for dynamic critical phenomena is used to discuss the EPR spectrum above the critical temperature of ferroelectrics and other structural transitions. The scaling properties of the spectrum are obtained. It is shown that splitting of the peak due to long-lived clusters may occur, and the temperature-dependence of the intensity and linewidth of these “cluster peaks” is estimated. The possible application of these results to corresponding recent experimental observations is out-lined, and a comparison to an alternative interpretation in terms of impurity effects is given.     

Non-newtonian effect near the critical point

In the presence of a shear flow the order parameter fluctuations are distorted and suppressed by the shear and there appears a new correlation length independent of temperature sufficiently near the critical point.     

Gravity influence on thermal relaxation near the critical point

Holographic interferometry measurements on a critical fluid sample performed during the D1 Spacelab flight reveal unexpected large density inhomogeneities under microgravity conditions. They are sustained by adiabatic temperature gradients and grow when approaching the critical point due to the diverging thermal expansion coefficient. Substantially increased relaxation time scales are found.     

Two-scale-factor universality near the critical point of fluids

Experimental evidence is presented in support of the validity of the hypothesis of two-scale-factor universality for the correlation function of fluids near the gas-liquid critical point. For Xe, SF₆, and CO₂, the dimensionless quantity $\text{R = ξ}{}_0\text{(}\text{B}{}^2\text{P}{}_{\mathrm{c}}\text{Γk}{}_{\mathrm{B}}\text{T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ is universal within the experimental accuracy of 10% and agrees with the value predicted by theory.     

Sign of kurtosis near the QCD critical point

We point out that the quartic cumulant (and kurtosis) of the order parameter fluctuations is universally negative when the critical point is approached on the crossover side of the phase separation line. As a consequence, the kurtosis of a fluctuating observable, such as, e.g., proton multiplicity, may become smaller than the value given by independent Poisson statistics. We discuss implications for the beam energy scan program at RHIC at BNL.     

Structure of liquid solutions near the critical point

Specific features of the structure of the critical state of binary liquid solutions leading to an anomalous behavior of the Rayleigh line due to a dramatic increase in concentration and density fluctuations are considered. It is shown that an experimental treatment must deal with two fluctuation regions near the critical point of solvent vaporization. In the first region, one can achieve a sufficient degree of accuracy by using theories like self-consistent field theory. In the second region, which is closer to the critical point than the first region, scaling theory of second-order phase transitions may be applied. It is found that the anomalous behavior of the Rayleigh line associated with kinetic coefficients is determined by the equilibrium thermodynamic properties and by the radius of fluctuation correlation (r_c). A general theory is developed for calculating thermodynamic potentials, especially the chemical potential and its concentration derivative in the fluctuation region. The results of these calculations are compared with the experimental data briefly described in the paper. Translated fromZhurnal Struktumoi Khimii, Vol. 39, No. 4, pp. 655–668, July–August, 1998.     

Nucleation in turbulent fluids near the critical point

Effects of turbulence on nucleation are investigated in classical fluids near the critical point. Turbulence can suppress the onset of nucleation, enhance the coagulation of droplets, and break up droplets. The final characteristic droplet size strongly depends on the temperature difference T_c − T and the Reynolds number Re.     

Sigma mesonic mode near the QCD critical point

Properties of the QCD critical point, an endpoint of the first order boundary line in the temperature T–baryochemical potential μ _B plane, are discussed with the Nambu–Jona-Lasinio model. It is demonstrated that the softening of the sigma mesonic mode is inherent to the crossover transition of the chiral symmetry while the spectral enhancement of the particle–hole mode near zero frequency is associated with the QCD critical point. Phenomenological implications in heavy-ion experiments are mentioned briefly.     

Growth rate of critical nuclei near the critical point of a fluid

The growth rate of critical nuclei for a fluid near its critical point is discussed on the basis of the stochastic equation for the probability distribution function of the local order parameter, which was derived previously by the author. The growth rate was found to depend on , the range of correlation of the order parameter fluctuation, andR, the radius of critical nuclei, as ⁰ R ^–3, in conformity with dynamical scaling. The rate of nucleation at the liquid-gas transition near the critical point is also discussed on the basis of this result.     

Magnetization of lutetium iron garnet near the critical point

A study has been made of the critical magnetic properties of lutetium iron garnet. Values of the critical exponents, β, δ and λ were seen to fulfill the scaling relation, β(δ?1)=λ, within the limits of experimental error. The critical temperature, obtained from the kink-point plot of applied magnetic field vs break-point temperature, was reaffirmed through utilization of the Kouvel-Fisher analysis.     

Finite-size behavior near the critical point of QCD phase-transition

It is pointed out that the finite-size effect is not negligible in locating the critical point of quantum colordynamics (QCD) phase transitions at current relativistic heavy ion collisions. The finite-size scaling form of the critical related observable is suggested. Its fixed point behavior at critical incident energy can be served as a reliable identification of a critical point and nearby boundary of QCD phase transition. How to experimentally find the fixed point behavior is demonstrated by using 3D-Ising model as an example. The validity of the method at finite detector acceptances at RHIC is also discussed.     

Singularities of the surface magnetisation profile near the critical point

Using renormalised perturbation theory we calculate explicitly the leading singular behaviour of the magnetisation shape function φ(y). To leading order φ(y)?y^σ, where σ=1-$\text{1}\text{6?}$.     

The soft-sphere model for metals near the critical point

Abstract

The soft-sphere model is convenient and accurate for predicting fluid phase thermodynamics. The validity of the model for describing the equation-of-state derivatives, Grüneisen's gamma and sound velocity, is shown.     

Density fluctuations and specific heat near the critical point

The density dependence of the proton magnetic shielding constants in liquid methanol and ethanol has been accurately measured at a temperature of 29.2°C and at external pressures between 1 and 2500 bar. For comparison, a measurement in the vapor coexisting with the liquid at 29.2°C has also been made. For the carbonyl protons the results appear to be in qualitative agreement with previous measurements of the density dependence of the shielding constants in methane and ethylene. The results are discussed theoretically on basis of the Buckingham electric field model.     

On anomalous diffusion of fractal clusters under certain realistic physical conditions

Summary Diffusion of a fractal cluster of dimensiond _f in a three-dimensional space is investigated. The diffusion process is assumed to be modelled by a standard parabolic diffusion equation, although a more general case represented by the Fokker-Planck-Kolmogoroff equation is also introduced. The mean-square displacement of the cluster mass centre is analysed and its anomalous behaviour is presented and critically discussed. The results obtained can be applied to describe some effects which may occur during the diffusion-limited cluster-cluster aggregation process, especially when the viscosity of the solvent is changed in time and/or a directed transport of clusters is present in the system. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.