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We calculate in two loop order the dynamical critical behavior at the tricritical point occuring in 3He-4He mixtures. Model F′ introduced by Siggia and Nelson (Phys. Rev. B 15:1427, [1977])—already problematic in one loop order—is shown in two loop order to lead to a divergence of the mass diffusion D in contradiction to experiments. Within the complex symmetric version of this model (model E⋆′) the dynamical critical exponents of the kinetic coefficients can be calculated exactly leading to a mass diffusion going to zero at the tricritical point as D(tX)∼tX1/2 (tX is the relative temperature distance at constant concentration) and the thermal diffusion ratio kT∼tX−1 diverges proportional to the concentration susceptibility in the experimental region. We also discuss effective dynamical critical exponents and compare them with recent simulations of the vector Blume-Emery-Griffths model.

An integral equation approach is developed to investigate phase coexistence properties of Ising spin fluids with Yukawa ferromagnetic and Lennard-Jones nonmagnetic interactions in the presence of an external field. The calculations are carried out on the basis of the Duh and Henderson closure with a specific Duh-like partitioning of the total potential. The coupled set of the Ornstein-Zernike equation, the closure relation and the external field constraint are solved using an efficient numerical algorithm. The phase diagrams are evaluated in a wide range of varying the external field and the ratio of strengths of Yukawa to Lennard-Jones interactions. Different types of the phase diagram topology as well as various external field dependencies of critical temperatures and densities are identified. The complexity with respect to simple Lennard-Jones fluids is explained by coupling between spatial and spin degrees of freedom in the system. A comparison of the obtained theoretical results with simulation data is made and a good agreement is observed.

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., Comment: 41 pages, 10 figures

The main aims of this paper are: (i) to present molecular dynamics (MD) results for time correlation functions, calculated with the help of a new symplectic algorithm that was proposed by us recently; (ii) to discuss the results obtained with the main focus on the interplay between the spin and liquid subsystems as well as on the influence of an external magnetic field on the properties of the system considered; (iii) to compare the time correlation functions, calculated in MD simulations, with theoretical predictions. Our results provide evidence of the interesting interplay of the two subsystems, causing new phenomena not found in nonmagnetic fluids and magnetic lattice models.

In these lectures, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range-correlated random-site disorder, and (iii) random anisotropy. Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of these lectures is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models., Lectures given at the Second International Pamporovo Workshop on Cooperative Phenomena in Condensed Matter (28th July - 7th August 2001, Pamporovo, Bulgaria). 51 pages, 12 figures, 1 style files included

Recent low-gravity measurements of the shear viscosity in xenon near its critical point are compared with theoretical results obtained within the field theoretical renormalization group (RG) theory. Nonasymptotic effects and gravity effects are included in our theoretical description, which allows a comparison outside the asymptotic region as well as with earthbound experiments affected by gravity. Comparisons are also made with the theoretical result of the mode coupling theory. In both theories no agreement with the frequency dependence of the real part of the shear viscosity within one-loop theory can be reached. The experimental value of the ratio of the imaginary part to the real part of the shear viscosity at Tc is found to be in agreement with the value calculated within the decoupled mode theory using the two-loop value for the critical exponent of the temperature dependence of the shear viscosity, but not with the one-loop value obtained in RG theory. Thus a complete two-loop calculation of the vertex function for the shear viscosity is required.

Six-loop massive scheme renormalization group functions of a d=3-dimensional cubic model (J.M. Carmona, A. Pelissetto, and E. Vicari, Phys. Rev. B vol. 61, 15136 (2000)) are reconsidered by means of the pseudo-epsilon expansion. The marginal order parameter components number N_c=2.862(5) as well as critical exponents of the cubic model are obtained. Our estimate N_c, 8 pages

Within mean field approximation we investigate the phase diagrams of magnetic fluids in presence of a magnetic field. In a finite field the magnetic phase transition is absent, but instead a line of first order liquid-liquid transitions ending in a critical point occurs for a magnetic interaction, which is sufficiently strong. Varying the magnetic field these critical points extend from the tricritical point at H=0 to a critical endpoint. For a fluid with Ising spins we calculate the critical lines and several tricritical exponents analytically. For Heisenberg fluids we obtain the phase diagrams from a numerical solution of the mean field equations of state.

Solid state systems exhibit besides usual second order phase transitions a rich variety of multicritical phenomena like Lifshitz points (or lines), tricritical points (or lines) and even tricritical Lifshitz points. Realizations of such points are numerous and were also verified in the family of ferroelectrics of the type (PbySn1y)2P2(SexS1-x)6. A review of the critical behavior at such points is presented here. Because of the importance of the uniaxial dipolar interaction in ferroelectrics the critical behavior is different from systems with short range interaction only. Moreover the coupling to the elastic degrees of freedom may not be neglected, and leads under certain conditions to a critical temperature dependence in certain elastic constants. Crossover phenomena, which are expected in the experimental accessible region of experiments are also considered.

We derive the nonasymptotic expressions for the frequency- and temperature-dependent sound velocity and sound absorption near a critical point in a mixture within renormalization group theory in one-loop order. The dynamic model considered is an extension of the corresponding model for pure fluids including concentration fluctuations. The theoretical result for the complex sound velocity is the same as at consolute points and gas-liquid critical points reflecting universality. Differences observed in the experiments at the two critical points mentioned are due to the different behavior of the sound velocity at ${T}_{c},$ which is finite in mixtures and zero in pure fluids, as well as due to nonasymptotic effects. Near the consolute point we compare our result with the phenomenological theory of Ferrell and Bhattacharjee [Phys. Rev. B 24, 4095 (1981); Phys. Rev. A 31, 1788 (1985)] and near the gas-liquid critical point with experiments in the ${}^{3}{\mathrm{H}\mathrm{e}\ensuremath{-}}^{4}\mathrm{He}$ mixture. A genuine dynamic parameter not considered so far and related to the critical enhancement of the thermal conductivity appears in the nonasymptotic expressions of the transport coefficients and the complex sound velocity. All nonuniversal background parameters of the complex sound velocity are fixed by a comparison of the corresponding theoretical expressions for the transport coefficients with experiments.

We compare the theoretical results of an explicit one loop calculation of the critical behavior of the sound propagation in pure liquids near the gas-liquid critical point, which has been derived within the field-theoretic renormalization group formalism, with experimental data in ${}^{3}$He, ${}^{4}$He, CO${}_{2}$, SF${}_{6}$, and Xe. The nonuniversal initial values of two dynamic model parameters, which are necessary for the calculation of all theoretical expressions, are determined by a fit of the shear viscosity at zero frequency in a small temperature region. The static quantities appearing in the theoretical expressions are taken from experiment. With these two dynamical initial values the temperature flow of the dynamic model parameters is completely determined. The sound attenuation and the sound velocity at arbitrary frequency as well as the thermal conductivity or the thermal diffusion coefficient may be calculated without any adjustable parameter. The parameter free predictions are in very good agreement with experimental results. This also holds for scaling plots of the reduced attenuation and dispersion taking into account the nonasymptotic behavior of the dynamic scale.

We calculate the hydrodynamic shear and sound mode near the liquid-gas phase transition and predict its values for different frequencies and temperatures. The dynamical parameters that enter the theoretical expressions are apart from static quantities the background values of the Onsager coefficients for the order parameter and the transverse momentum current. We find within the field-theoretical renormalization group formalism the asymptotic scaling functions or the real and imaginary parts of the shear and sound mode in the $\ensuremath{\omega}$-${\ensuremath{\xi}}^{\ensuremath{-}1}$ plane. Our main concern, however, is the calculation of the nonasymptotic expressions describing the crossover from the analytic background to the asymptotic critial behavior.

On the basis of our previous results (Physica A 220 (1995) 325) the collective mode spectrum of the Heisenberg ferrofluid model is studied in the hydrodynamic region. We start from the rigorous microscopic approach taking into account all conserved quantities and calculate the explicit expressions for the dispersion and damping coefficient of sound modes. It is shown that the sound velocity of Heisenberg ferrofluid at constant external magnetic field is isotropic and can be expressed by the adiabatic compressibility at constant magnetization m . We also calculate the heat and spin modes which are purely diffusive. Explicit expressions for the viscosity, thermal conductivity, spin diffusion and thermomagnetic diffusion coefficients containing time correlation functions are derived. Our results are compared with previous ones obtained mainly within phenomenological theories.

We examine the equation of state of liquid4He at negative pressures close to the spinodal density ϱs where the hydrodynamic speed of sound vanishes. The non-analytic behavior of the equation of state and the speed of sound in the vicinity of the spinodal density are calculated in two and in three dimensions; we find for the speed of sound the non-analytic behavior mc s 2 ∼ (ϱ — ϱs)2/5 in three dimensions and mc s 2 ∼[(ϱ-ϱs)/¦ln(ϱ-ϱs)¦]1/2 in two dimensions. We then examine the low density regime numerically, using a semi-analytic microscopic theory. It is found that non-analytic exponents are visible only in a negligible density regime around the spinodal point. Estimates for the spinodal densities, and the range of critical fluctuations are provided.

Using Zubarev's method of nonequilibrium statistical operator, the generalized hydrodynamic equations are obtained for a model of magnetic liquid in an inhomogeneous external field. In this model the “liquid” subsystem is treated as a classical one and the “magnetic” subsystem is described by quantum mechanical methods. The properties of the transport equations are analysed in the case of a weak nonequilibrium. The equations for time correlation functions and collective mode spectrum are also found in the same manner. It is shown that the generalized hydrodynamic equations reduce to the well-known results in the limiting cases when the dynamic variables of one subsystem are formally neglected. As an illustration, a simple model of spin relaxation is considered, and the frequency matrix and the matrix of memory functions are calculated. A comparison with previous works is made.

The critical behavior near consolute points and plait points in mixtures and along lines connecting such points in the phase diagram belongs to the universality class of gas-liquid transitions in pure liquids. We give a survey of the results for the temperature dependence of transport coefficients, thermal conductivity, mass diffusion, and thermal-diffusion ratio, in mixtures within a non-asymptotic renormalization-group theory of critical dynamics. The observable critical behavior in some cases is nonuniversal and may be strongly concentration dependent. This is explained by different crossover temperatures in the singular Onsager coefficient of the order parameter and in the hydrodynamic transport coefficients. At the plait point the value of (ie1363-01) determines the crossover to the asymptotic behavior in the transport coefficients, and its smallness explains the situation in3He-4He mixtures. We also consider ionic solutions, where long-range forces may be present. The dynamical universality class in this case is different from that of mixtures with short-range interaction. As well as the “classical” static behavior for sufficient long-range interaction potentials, the dynamical critical behavior depends on the exponent of the power law for the spatial decrease in this interaction. This offers an additional possibility to determine this exponent by measuring the temperature dependence of the hydrodynamic transport coefficients.

This article concludes a series of papers (R. Folk, Yu. Holovatch, and G. Moser, Phys. Rev. E 78, 041124 (2008); 78, 041125 (2008); 79, 031109 (2009)) where the tools of the field theoretical renormalization group were employed to explain and quantitatively describe different types of static and dynamic behavior in the vicinity of multicritical points. Here, we give the complete two loop calculation and analysis of the dynamic renormalization-group flow equations at the multicritical point in anisotropic antiferromagnets in an external magnetic field. We find that the time scales of the order parameters characterizing the parallel and perpendicular ordering with respect to the external field scale in the same way. This holds independent whether the Heisenberg fixed point or the biconical fixed point in statics is the stable one. The non-asymptotic analysis of the dynamic flow equations shows that due to cancelation effects the critical behavior is described - in distances from the critical point accessible to experiments - by the critical behavior qualitatively found in one loop order. Although one may conclude from the effective dynamic exponents (taking almost their one loop values) that weak scaling for the order parameter components is valid, the flow of the time scale ratios is quite different and they do not reach their asymptotic values., 22 pages, 7 figures. Revised version, references updated, Fig. 5 modified, typos corrected

A complete two loop renormalization group calculation of the multicritical dynamics at a tetracritical or bicritical point in anisotropic antiferromagnets in an external magnetic field is performed. Although strong scaling for the two order parameters (OPs) perpendicular and parallel to the field is restored as found earlier, in the experimentally accessible region the effective dynamical exponents for the relaxation of the OPs remain different since their equal asymptotic values are not reached., Comment: 6 pages, 2 figures; some additions, corrected typos

A mesoscopic description of various systems containing spherical charged particles in solvent inducing effective attraction is developed by a systematic coarse‐graining procedure. For weak ordering the theory can be reduced to the Landau‐Ginzburg or the Landau‐Brazovskii field theory, depending on the form of the effective interactions between particles. Within the framework of this theory we obtain and discuss the λ‐line and the universal sequence of phases: disordered, bcc, hexagonal, lamellar, inverted hexagonal, inverted bcc, disordered, for increasing density well below the close‐packing density. The sequence of phases agrees with experimental observations and with simulations of many self‐assembling systems. In addition to the above phases, more complex phases may appear depending on the interaction potentials. For a particular form of the short‐range attraction long‐range repulsion potential we find the bicontinuous gyroid phase (Ia3d symmetry) that may be related to a network forming cluster of colloids in a mixture of colloids and nonadsorbing polymers.

The possibility of realizing a superfluid state of bound electron‐hole pairs (magnetoexcitons) with spatially separated components in a graphene double layer structure (two graphene layers separated by a dielectric layer) subjected to a strong perpendicular to the layers magnetic field is analyzed. We show that the superfluid state of magnetoexcitons may emerge only under certain imbalance of filling factors of the layers. The imbalance can be created by an electrostatic field (external gate voltage). The spectrum of elementary excitations is found and the dependence of the Berezinskii‐Kosterlitz‐Thouless transition temperature on the interlayer distance is obtained. The advantages of using the graphene double layer systems instead of double quantum well GaAs heterostructures are discussed.

We discuss a simple version of Landau theory with two single‐component order parameters, P and M, corresponding to the ferroelectric and ferromagnetic phases coupled to each other via a −|λ|P2M2 term. In the case of ferroelectricity appearing at a temperature Tf much higher than that of a ferromagnetic transition, the latter is strongly renormalized (TM→TRM>> TM). The thermodynamics of the model in spatially homogeneous phases is elaborated first. Our simple formulation is applied next to BiMnO3 and provides a good semiquantitative description of the magnetic and dielectric properties except for the specific heat, which is not entirely explained in the regime T≈TRM even when the Gaussian fluctuations of the order parameters are included. Possible improvements to our approach are briefly discussed.

The ferroelectric phase transition in Sn2P2S6 crystals is a result of a strong non‐linear interaction between vibrational modes with Bu and Ag symmetry which determines the three‐well shape of the potential. Such multistability is reflected in spectroscopic and thermodynamic characteristics of the lattice anharmonicity. By analysing the quasielastic and Brillouin light scattering, heat capacity, volume thermal expansion and heat transport temperature behavior, it was found that negative contribution of the optic modes to the Gruneisen coefficient in a wide temperature interval of the ferroelectric phase is special characteristic of the investigated ferroelctrics.

The solvation force for two‐dimensional Ising stripes in the presence of boundary fields is calculated via exact diagonalization of the transfer matrix in two cases: the symmetric case corresponds to identical boundary fields and the antisymmetric case to exactly opposite boundary fields. In the symmetric case the solvation force is always negative (attractive), while in the antisymmetric case it is positive (repulsive) at high temperatures and negative at low temperatures. It changes sign close to the critical wetting temperature characterizing the semi‐infinite system. The properties of the solvation force are discussed, and the scaling function describing its dependence on temperature, boundary field, and stripe’s width is proposed.

The problem of phase transitions in a system of particles with finite value of the lifetime is analyzed. As an example the theory of condensation of indirect excitons in semiconductor double quantum wells is presented. For description of a spatial distribution of condensed and gas phases two models of phase transitions are used: the model of nucleation and growth and the model of spinodal decomposition generalized on unstable particles. It is shown that due to finite value of the exciton lifetime the sizes of condensed phases are restricted and in two‐dimensional case, the regions of condensed phase have the shape of islands located within the excitonic gas. There is specific interaction between islands of the condensed phase through exciton concentration fields. This interaction causes the development of different structures of exciton condensed phases in the crystal irradiated by light. The evolution of the islands of condensed phase is studied depending on the changes of the temperature, pumping and th...

For a system of interacting quantum anharmonic (double‐welled) oscillators (quantum anharmonic crystal), it is shown that a phase transition can cause the equilibrium dynamics of a given oscillator to be reducible. This means that the oscillator prefers one of the wells. Sufficient conditions for this effect to occur at some temperature, or not to occur at all temperatures, are presented.

An open question in the study of the spin‐1/2 Ising model is the solution of the two‐dimensional case in the presence of a magnetic field. A possible answer is based on the study of L‐coupled linear chains in the limit of large L. Results reported in the literature show that a dimensional crossover from the one to the two dimensional model does not exist. However, what happens if one considers open boundary conditions (BC)? In this article I show that, for an appropriate choice of the BC, a system of L‐chains exhibits a ferromagnetic order characterized by a critical temperature which, for zero magnetic field, tends to the Onsager’s one as L increases. It is then possible to study the phase diagram in the (h, T) plane and obtain a solution for finite magnetic field.

We study the effects of size and charge asymmetry on the gas‐liquid critical parameters of a primitive model (PM) of ionic fluids. The model is characterized by the two parameters: hard‐sphere diameter‐, λ = σ+/σ− and charge, z = q+/|q−|, ratios of the two ionic species. Using the collective variables based theory we calculate the critical temperature and the critical density for the two versions of PM: an equisize PM with charge asymmetry (λ = 1, z≠1 and a monovalent PM with size asymmetry (λ≠1, z = 1). The trends obtained for the both critical parameters of the models under consideration agree qualitatively with Monte Carlo simulation findings.

The quasi‐stationary electron states are studied in the three‐barrier resonance‐tunnel structure which is the basic element of coherent quantum cascade lasers. In the models of rectangular and δ‐barrier potentials there is established theory of evolution and collapse of double resonance complexes in a symmetric resonance‐tunnel structure. The induced conductivity of nano‐system is calculated within the both models. It is shown that the negative induced conductivity of three‐barrier resonance‐tunnel structure in δ‐barrier model is dozens times smaller than more realistic magnitudes obtained within the rectangular potentials model.

An integral-equation approach is developed to study interfacial properties of anisotropic fluids with planar spins in the presence of an external magnetic field. The approach is based on the coupled set of the Lovett-Mou-Buff-Wertheim integro-differential equation for the inhomogeneous anisotropic one-particle density and the Ornstein-Zernike equation for the orientationally dependent two-particle correlation functions. Using the proposed inhomogeneous angle-harmonics expansion formalism we show that these integral equations can be reduced to a much simpler form similar to that inherent for a system of isotropic fluids. The interfacial orientationally dependent direct correlation function can be consistently constructed by means of a nonlinear interpolation via its values obtained in the coexisting anisotropic bulk phases. A soft mean spherical approximation is employed for the closure relation. This has allowed us to solve the complicated integral equations in the situation when both spatial inhomogeneity and orientational anisotropy are present simultaneously. The approach introduced is applied to an XY fluid model with ferromagnetic spin interactions. As a result, the density-orientation and magnetization profiles at the liquid-vapor interfaces are calculated in a wide range of temperatures up to subcritical regions. The influence of the external field on the microscopic structure of the interfaces and the surface tension is also analyzed in detail.

We calculate the relaxational dynamical critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry including conservation of magnetization by renormalization group (RG) theory within the minimal subtraction scheme in two loop order. Within the stability region of the Heisenberg fixed point and the biconical fixed point strong dynamical scaling holds with the asymptotic dynamical critical exponent $z=2\phi/\nu-1$ where $\phi$ is the crossover exponent and $\nu$ the exponent of the correlation length. The critical dynamics at $n_\|=1$ and $n_\perp=2$ is governed by a small dynamical transient exponent leading to nonuniversal nonasymptotic dynamical behavior. This may be seen e.g. in the temperature dependence of the magnetic transport coefficients., Comment: 6 figures

The field-theoretical gauge model for a superconductor, generalized to a {ital n}/2-component complex order parameter, is renormalized in two-loop order. The question of a fluctuation-induced first-order transition is discussed, and the crossover functions for the effective exponents and the amplitude ratio of the specific heats above and below {ital T}{sub {ital c}} are given.

The microscopic structure and thermodynamic properties of liquid-vapor and liquid-liquid interfaces in Ising fluids are studied using an integral equation approach. The calculations are performed in the absence and presence of an external magnetic field by solving the corresponding set of Lovett-Mou-Buff-Wertheim integrodifferential equations for the one-particle density distribution functions. The two-particle inhomogeneous direct correlation functions are consistently constructed by nonlinear interpolation between the bulk ones. The bulk correlation functions of the coexisting phases are obtained from the Ornstein-Zernike equations with a modified soft mean spherical approximation for the closure relation. As a result, the density and magnetization profiles at liquid-vapor and liquid-liquid interfaces as well as the surface tension and adsorption coefficients are evaluated in a wide temperature range including subcritical regions. The influence of an external magnetic field on the liquid-vapor interfaces is also considered.

Using Monte Carlo simulation techniques, we study the ferromagnetic order-disorder phase transition in Ising spin fluids with hard-core Yukawa interaction truncated at various cutoff radii r{c}. We focus our interest on the dependence of critical quantities such as the Binder cumulant and various exponent ratios on the value of r{c}, and on the question whether the Fisher-renormalized exponents expected for such systems can be observed in the simulations. It turns out that the corrections to scaling decaying with a rather small exponent prevent reaching the asymptotic region with the computational power available. Thus, we observe only effective exponents, with different (nonuniversal) values depending on the cutoff radius. The same behavior is also found for the critical Binder cumulant. Nevertheless, an exact investigation of the effective susceptibility exponent gamma{eff} as a function of temperature seems to point towards a Fisher-renormalized value. For two selected cutoff radii, the critical temperature is determined more accurately using, in addition to the cumulant crossing technique, the scanning technique and the shifting technique, taking into account corrections to scaling. Simulations of Ising fluids with constant cutoff radius and varying Yukawa-tail screening lengths lambda also show a nonuniversal dependence of U{c} on lambda. Finally, we have performed simulations of the Ising lattice model with increasing number of couplings which show the expected asymptotic behavior, independent of the range of interactions.

The phase behavior of Ising spin fluids is studied in the presence of an external magnetic field with the integral equation method. The calculations are performed on the basis of a soft mean spherical approximation using an efficient algorithm for solving the coupled set of the Ornstein-Zernike equations, the closure relations, and the external field constraint. The phase diagrams are obtained in the whole thermodynamic space including the magnetic field H for a wide class of Ising fluid models with various ratios R of the strengths of magnetic to nonmagnetic Yukawa-like interactions. The influence of varying the inverse screening lengths z(1) and z(2), corresponding to the magnetic and nonmagnetic Yukawa parts of the potential, is investigated too. It is shown that changes in R as well as in z(1) and z(2) can lead to different topologies of the phase diagrams. In particular, depending on the value of R, the critical temperature of the liquid-gas transition either decreases monotonically, behaves nonmonotonically, or increases monotonically with increasing H. The para-ferro magnetic transition is also affected by changes in R and the screening lengths. At H=0, the Ising fluid maps onto a simple model of a symmetric nonmagnetic binary mixture. For H--> infinity, it reduces to a pure nonmagnetic fluid. The results are compared with available simulations and the predictions of other theoretical methods. It is demonstrated that the mean spherical approximation appears to be more accurate compared with mean field theory, especially for systems with short ranged attraction potentials (when z(1) and z(2) are large). In the Kac limit z(1), z(2) -->+0, both approaches tend to nearly the same results.

We investigate the asymptotic and effective static and dynamic critical behavior of (d=3)-dimensional magnets with quenched extended defects, correlated in $\epsilon_d$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d-\epsilon_d$ dimensions. The field-theoretical renormalization group perturbative expansions being evaluated naively do not allow for the reliable numerical data. We apply the Chisholm-Borel resummation technique to restore convergence of the two-loop expansions and report the numerical values of the asymptotic critical exponents for the model A dynamics. We discuss different scenarios for static and dynamic effective critical behavior and give values for corresponding non-universal exponents., Comment: 12 pages, 6 figures

We present phase diagrams that were calculated both in mean-field theory and via Monte Carlo (MC) simulations for binary mixtures of a ferromagnetic Ising fluid and a nonmagnetic fluid (Ising mixtures) in the absence of an external field. We look at both the simple ideal Ising mixture, consisting of an ideal Ising fluid and a hard-sphere fluid, as well as at the general case with one component being a nonideal Ising fluid and the other a van der Waals fluid. It is shown that the mean-field phase diagram of the ideal Ising mixture in the limit of infinite pressure is identical to that of the Blume-Capel model for $^{3}\mathrm{He}\ensuremath{-}^{4}\mathrm{He}$ mixtures. The MC phase diagrams were obtained using the Gibbs ensemble, the cumulant intersection technique, and the multihistogram reweighting method, adapted to the semigrand ensemble. The results are qualitatively compared with mean-field theory, and both types of tricritical lines occurring there are verified in the computer simulations.

A method of integral equations is developed to study inhomogeneous fluids with planar spins in an external field. As a result, the calculations for these systems appear to be no more difficult than those for ordinary homogeneous liquids. The approach proposed is applied to the ferromagnetic XY spin fluid in a magnetic field using a soft mean spherical closure and the Born-Green-Yvon equation. This provides an accurate reproduction of the complicated phase diagram behavior obtained by cumbersome Gibbs ensemble simulation and multiple histogram reweighting techniques., 4 pages, 3 figures, submitted to Phys. Rev. Lett

The influence of an external magnetic field on the liquid-gas phase transition in Ising, XY, and Heisenberg spin fluid models is studied using a modified mean field theory and Gibbs ensemble Monte Carlo simulations. It is demonstrated that the theory is able to reproduce quantitatively all characteristic features of the field dependence of the critical temperature T_c(H) for all the three models. These features include a monotonic decrease of T_c with rising H in the case of the Ising fluid as well as a more complicated nonmonotonic behavior for the XY and Heisenberg models. The nonmonotonicity consists in a decrease of T_c with increasing H at weak external fields, an increase of T_c with rising H in the strong field regime, and the existence of a minimum in T_c(H) at intermediate values of H. Analytical expressions for T_c(H) in the large field limit are presented as well. The magnetic para-ferro phase transition is also considered in simulations and described within the mean field theory., 14 pages, 12 figures (to be submitted to Phys. Rev. E)

We study a binary mixture of a van der Waals fluid and a ferromagnetic fluid at zero magnetic field on the basis of the mean field Ising fluid model and the van der Waals theory with quadratic mixing rules. Depending on three reduced parameters, the phase diagram shows a surface of magnetic phase transitions and lines of tricritical points, critical end points, and magnetic consolute points. First-order phase transition surfaces and critical lines are calculated numerically. For the line of tricritical points, which can occur in two different topologies, an analytic expression is derived. All higher-order lines and coexistence surfaces are visualized in three-dimensional x, T, p and $\ensuremath{\xi},$ T, p diagrams, where $\ensuremath{\xi}$ is a mapping of $\ensuremath{\Delta},$ the conjugated field of the mole fraction x, on the unit interval.

The influence of a local anisotropy of random orientation on a ferromagnetic phase transition is studied for two cases of anisotropy axis distribution. To this end a model of a random anisotropy magnet is analyzed by means of the field theoretical renormalization group approach in two loop approximation refined by a resummation of the asymptotic series. The one-loop result of Aharony indicating the absence of a second-order phase transition for an isotropic distribution of random anisotropy axis at space dimension $d

The effect of fluctuation induced weakly first order phase transition known for three dimensional (3D) type I superconductors appears in a modified and strongly enhanced variant in thin (quasi-2D) superconducting films. The unusual thermodynamic properties of this new type of first order phase transitions and the possibility for an experimental verification of the effect are established and discussed.

Using thermodynamic arguments treatment it is shown that, independently on whether Fisher renormalization changes the critical exponents near a phase transition in a constrained system or not, new corrections to scaling with correction exponents proportional to the specific heat index $\alpha$ appear. Because of the smallness $\alpha$ for the Ising, the XY, and the Heisenberg universality classes these corrections are dominant and can cause strong crossover effects. It is proven that the appearance of Fisher corrections to scaling is a quite general feature of the systems with constraints., Comment: 6 pages; submitted to Physica A

We calculate the critical behavior of the transport coefficients at the liquid-vapor critical (plait) point in a mixture. The dynamical equations without first sound reduce to the model H' of Siggia, Halperin and Hohenberg. We treat model H' within the field theoretic renormalization group theory. It is shown that the plait point belongs to the same universality class like the pure liquid and the consulate point. Asymptotically we find the thermal conductivity finite at Tc, the mass difusion D goes to zero like tγ−xλν, the thermal diffusion ratio kT diverges like t-γ+xλν and the shear viscosity diverges like t-xην. We also consider the non asymptotic behavior, which is important in the comparison with experiments.

We calculate the hydrodynamic transport coefficients above the superfluid transition within the renormalized field theory of the complete model of Siggia and Nelson. The main improvement in the comparison with the experiment at higher concentrations of 3 He comes from the proper treatment of the temperature dependence of the static quantities.