Percus-Yevick equation for an inhomogeneous fluid: Critical region

The critical region of a locally nonuniform fluid with gaussian density inhomogeneity is investigated. Nonclassical behaviour is found; critical exponents agree very well with those obtained from the perturbation theory of liquids. The action of an external field shifts the critical region and weakens the critical behaviour. Discussed effects could be verified experimentally.     

Criticality of Epidemic Spreading in Mobile Individuals Mediated by Environment

We investigate the critical behaviour of an epidemical model in a diffusive population mediated by a static vector environment on a 2D network. It is found that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. Finite-size and short-time dynamic scaling relations are used to determine the critical population density and the critical exponents characterizing the behaviour near the critical point. The results are compatible with the universality class of directed percolation coupled to a conserved diffusive field with equal diffusion constants.     

A correlation measure in non-equilibrium phase transitions

Bit-number cumulants of a probability distribution give ordered measures of correlations between subsystems. Especially the second one, the bit-number variance (which in equilibrium is connected with specific heat) is discussed with respect to its critical behaviour for special non-equilibrium phase transitions in chemical reaction systems. Also in non-equilibrium the critical behaviour indicates critical correlations.     

Renormalized tricritical behaviour for wetting transitions

In this paper we study tricritical wetting behaviour in three dimensions. In particular we concentrate on systems with short-ranged forces and apply linear functional renormalization group techniques to elucidate the effect of fluctuations upon tricriticality. In comparison with studies of critical wetting we identify an additional fluctuation regime which is relevant for values of the capillary parameter between 2/9 and 1/2. We demonstrate that this regime essentially provides a crossover from mean-field like behaviour, in which tricritical exponents are always distinct from their critical counterparts, from intermediate- and strong-fluctuation behaviour where the critical exponents for tricritical and critical wetting are found to always coincide. We conclude by discussing briefly the possible relevance of these results for experimental studies of wetting. Received 4 January 2001 and Received in final form 11 May 2001     

A characteristic critical quantity in nonequilibrium phase transitions

The bit-number variance, a generalization of specific heat, which was already introduced in earlier papers [7-10] is discussed, with respect to the critical behaviour in equilibrium-and nonequilibrium phase transitions. In the considered mean field examples it shows a uniform behaviour dependent on to which of two classes the system belongs. With it a new characteristic critical quantity is found appropriate for the comparison of different nonequilibrium phase transitions. New arguments are given with respect to the connection between critical correlations and the bit-number cumulants.     

On the zero-temperature critical behaviour of the quantum X-Y model in a transverse magnetic field

It is shown that the zero-temperature critical behaviour of the quantum-mechanical X-Y spin model in a transverse magnetic field is characterized by pure gaussian critical exponents. Remarks on the university of the quantum critical behaviour are also made.     

Thermodynamic stability of equilibrium system and critical state

On the basis of general Gibbs conditions of stability, the requirements of critical state stability that are applied to adiabatic coefficient of stability (ACS) and their derivatives are obtained. The examination of these conditions with critical state definition establishes the existence of four alternative types of critical behaviour of the thermodynamic system. These types are classified by the critical behaviour of ACS and K_C, which is connected with ACS. Analysis of the asymptotic behaviour of adiabatic quantity (AQ), which is consistent with stability requirements, demonstrates that both analytic and nonanalytic behaviours are possible.     

A sharp transition between a trivial 1D BTW model and self-organized critical rice-pile model

A one-dimensional model of a rice-pile is numerically studied for different driving mechanisms. We found that for a sufficiently large system, there is a sharp transition between the trivial behaviour of a 1D BTW model and self-organized critical (SOC) behaviour. Depending on the driving mechanism, the self-organized critical rice-pile model belongs to two different universality classes. Received 18 December 1998     

Critical behaviour of the specific heat of La0.9Ag0.1MnO3 manganite

 For the first time the specific heat of polycrystalline La_0.9Ag_0.1MnO₃ manganite near the Curie temperature was precisely measured by AC calorimetry and its critical behaviour was studied. The critical behaviour of the specific heat was approximated by the relationship taking into account corrections to the scaling. The regularities of variations in the universal critical parameters near the critical point are determined, and their values are calculated. Detailed analysis and comparison of the received results with the theoretical predictions and other experimental results was carried out.     

MSA for segregating liquid mixtures: Crossover from mean-spherical to mean-field exponents

The critical exponents , , and of a binary mixture of equal-sized hard spheres with repulsive Yukawa interactions for unlike-atom pairs and attractive Yukawa interactions for like-atom pairs are calculated from analytical solutions in the mean spherical approximation. For strong to moderate screening we find the expected mean spherical values of the critical exponents; for weak screening the system shows a mean field behaviour. For an intermediate range of the potential, the system displays a crossover from mean-field behaviour to mean-spherical behaviour in the immediate vicinity of the critical point. The domain over which the mean-spherical exponents describe the critical behaviour shrinks as the range of the interatomic potential increases.     

Critical behaviour of random compressible magnets

The critical properties of a compressible random magnet are studied using renormalization group methods. Then-component orderparameter is coupled to quenched disorder and to the elastic fluctuations of the anisotropic solid. It is shown, that the critical behaviour of a compressible random magnet is in general the same as that of a random magnet on a rigid lattice. However, if the specific heat exponent of the ideal magnet is positive and the disorder is sufficiently weak, a macroscopic instability may prevent the system in reaching the critical point. The resulting first-order transition may be preceded by pseudocritical behaviour characteristic to pure compressible magnets. The effect of random magnetic fields on the critical properties of compressible magnets is also discussed.     

Josephson junctions based on c-axis oriented YBaCuO/PrBaCuO/YBaCuO trilayers

We have fabricated sandwich SNS (superconductor/normal metal/superconductor) junctions using in-situ grown c-axis oriented YBaCuO/PrBaCuO/YBaCuO trilayers. We observe supercurrents for PrBaCuO thicknesses up to 130 nm at 4.2 K. To confirm or rule out the presence of shorts through the barrier, the junction behaviour has been further characterised. Magnetic-field and PrBaCuO thickness dependences of the critical current, as well as a correct scaling with the junction area of both the critical current and the normal resistance, appear to indicate a reasonable uniformity for the barriers on the scale of the size of the junctions, typically 10 μm. These results suggest that either we are observing real c-axis transport in PrBaCuO or, if the behaviour is defect dominated, that the criteria commonly used to demonstrate good device behaviour should be applied carefully. The temperature dependence of the junction critical current and normal resistance are also reported and compared.     

Conserved Manna model on Barabasi–Albert scale-free network

In this paper, a conserved Manna model is constructed and studied on Barabasi–Albert scale-free network with degree exponent γ = 3. Numerically I show that the system undergoes an absorbing state phase transition when the particle density is varied. Such a phase transition is characterized by measuring several critical exponents associated with the critical behaviour of the model. It has been found that the critical exponents exhibit mean field values of directed percolation. At the critical point, the spreading exponents have also been estimated. They satisfy the usual scaling relations. The effect of various initial conditions has been investigated and the result found to be independent of initial conditions, contrary to the fact that critical behaviour of such model highly depends on initial conditions when studied on regular lattice. The study confirms that though the Manna model in the lower dimensions exhibits different critical behavior other than DP, in the scale-free network it exhibits similar mean field result of DP class.     

Closed-loop liquid-liquid equilibria and the global phase behaviour of binary mixtures involving hard-sphere + van der Waals interactions

Calculations of the critical properties of binary mixtures of components of equal size are reported using the Guggenheim equation of state. The calculations are used to determine the global phase diagram of binary mixtures. Type VI phase behaviour is predicted successfully indicating that closed-loop liquid-liquid equilibria can be obtained from hard-sphere + van der Waals interactions. Closed-loop liquid-liquid equilibria occur in the region of the global phase diagram characterized by moderately strong unlike interactions and components with very dissimilar critical temperatures. The Guggenheim equation can predict all experimentally known phase behaviour types. In addition, other hypothetical phase behaviour types are also predicted.     

Critical dynamics in the presence of relaxing defects

The influence of defects coupling linearly to the order parameter on the critical behaviour of structural phase transitions is studied. A continuum model for the statics and dynamics is introduced and is investigated by the renormalization group theory. If the defects are slow a central peak is found, the characteristic width of which is determined by the defects. Concerning the critical behaviour the dynamical model belongs to the same universality class as the one studied previously by Grinstein, MA, and Mazenko. The concentration dependence of the central peak response is discussed inside and outside the critical region.     

The spectrum of depolarized light scattered from a critical nitrobenzene-n-hexane mixture

Both linewidth and intensity measurements have been performed on the depolarized reorientation spectrum of a critical mixture of nitrobenzene-n-hexane. No critical behaviour of the linewidth or intensity was observed. The measurements are in very good agreement with all extrapolated data or expected values for binary nitrobenzene mixtures far from their critical point.     

Influence of the experimental conditions on the specific heat critical behaviour of TGS

Using a conduction calorimeter the specific heat critical behaviour of a TGS crystal has been measured. The ranges of the deviations from the classical behaviour below and above the transition point are 1 and 20 K respectively. These deviations seem to be well related to LK theory predictions. In a range of 0.1 K below the transition point thermal hysteresis appears which does not depend on the measuring temperature rate. The same behaviour is obtained with the sample at atmospheric pressure and under a high vacuum.     

Critical properties of random anisotropy magnets

The problem of critical behaviour of three dimensional random anisotropy magnets, which constitute a wide class of disordered magnets is considered. Previous results obtained in experiments, by Monte Carlo simulations and within different theoretical approaches give evidence for a second order phase transition for anisotropic distributions of the local anisotropy axes, while for the case of isotropic distribution such transition is absent. This outcome is described by renormalization group in its field theoretical variant on the basis of the random anisotropy model. Considerable attention is paid to the investigation of the effective critical behaviour which explains the observation of different behaviour in the same universality class.     

The 44th Physical Society Exhibition, 1960: (2) The physical society colour group's exhibition

During the last decade considerable effort has been expended in the study of critical phenomena. These investigations are especially rewarding because they provide important links between several diverse branches of physics. For example, antiferromagnets, pure fluids, binary solutions and alloys all exhibit analogous critical behaviour. It is now firmly established that the classical phenomenological theories that have been proposed to describe these systems fail in the critical region: mainly because they do not account for the fluctuation phenomena which occur close to critical points, and are a poor approximation for systems with shortrange forces. Considerable progress has been made in formulating more realistic models, for example the king and Heisenberg ferromegnets, and some success has been achieved in obtaining solutions for these models. Similar theories may be postulated to describe the critical behaviour of other systems. Recent progress in theoretical understanding and refinement of experimental techniques have helped to stimulate interest in the subject, and today the study of critical phenomena is one of the most promising and rapidly advancing areas of physics.