On the critical behaviour of Bose systems at constant density

The scaling behaviour of Bose systems at constant density is studied using the ?-expansion method. The chemical potential and equation of state are obtained in terms of t = (T ? T_c)/T_c to first order in ?.     

Ising-type exchange interaction in two-level optical systems

It is shown that the indirect interaction of pseudospins via radiation field in a two-level optical system contains pseudospin energy components of the Ising exchange-interaction type. The conditions under which this interaction can show up in optical spectra are discussed.     

Local waiting times in critical systems

The quiet times at a fixed point in space are investigated in a system close to or at a non-equilibrium phase transition. The statistics for such first-return times follow from the universality class of the dynamics and the ensemble: for a power-law waiting time distribution the exponent depends on the dimension and the underlying model. We study the two-dimensional Manna sandpile, with both the continously driven self-organized version and the tuned one. The latter has an absorbing state or depinning phase transition at a critical value of the control parameter. The connection to a driven interface in a random medium gives the exponent of the waiting time distribution. In the open ensemble, differences ensue due to the spatial inhomogeneity and the properties of the driving signal. For both ensembles, the waiting time distributions are found to exhibit logarithmic corrections to scaling.Received: 13 September 2004, Published online: 23 December 2004PACS: 05.70.Ln Nonequilibrium and irreversible thermodynamics - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 52.25.Fi Transport properties     

Inhomogeneous systems with unusual critical behaviour

The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are considered as well as general parabolic shapes. In the other case the system contains defects, either narrow ones in the form of lines or stars, or extended ones where the couplings deviate from their bulk values according to power laws. In each case the perturbation may be irrelevant, marginal or relevant. In the marginal case one finds local exponents which depend on a parameter. In the relevant case unusual stretched exponential behaviour and/or local first-order transitions appear. The discussion combines mean field theory, scaling considerations, conformal transformations and perturbation theory. A number of examples are Ising models for which exact results can be obtained. Some walks and polymer problems are considered, too.     

On the critical behaviour of disordered systems

It is shown by general renormalization group analysis that in disordered systems there is no quasi-homogeneous critical behaviour with positive specific-heat exponent α.     

Field theory of critical behaviour in driven diffusive systems

We present a field theoretic renormalisation group study for the critical behaviour of a diffusive system with a single conserved density subjected to an external driving force. The anisotropies induced by the external field require the introduction of two critical parameters associated with transverse and longitudinal order. The transition to transverse order is governed by a fixed point which is infrared stable below five dimensions. With the help of Ward-Takahashi identities based on Galilei invariance, we derive scaling forms for density correlation functions, critical exponents to all orders in =5–d, and the equation of state, taking care of a dangerous irrelevant composite operator. The transition is continuous and of mean-field type, with anomalous long-wavelength and long-time correlations in the longitudinal direction only. For the transition to longitudinal order, no infrared stable fixed point is found. An analysis of the mean-field equations indicates that the transition is discontinuous.     

Non-universal critical behaviour in mean-field theory of inhomogeneous systems

We consider the layered magnetic systems with inhomogeneous inter-layer couplings and study their critical properties within the framework of mean-field theory. We consider two kinds of distribution of the couplings: (i) quasi-periodic, according to the Fibonacci sequence and (ii) smoothly inhomogeneous, in which the couplings deviate from the bulk couplings by an amount of Al⁻², where l measures the distance from a free surface. According to analytical and accurate numerical results the critical behaviour of both the problems is non-universal and the corresponding critical exponents are coupling dependent.     

Ising-type critical exponents of the fully frustrated spin-1/2 Heisenberg FM/AF square bilayer at a critical magnetic field

The fully frustrated spin-1/2 Heisenberg FM/AF square bilayer in a magnetic field with the ferromagnetic inter-dimer interaction and the antiferromagnetic intra-dimer interaction is explored by the use of localized many-magnon approach, which allows to connect the original purely quantum Heisenberg spin model on a square bilayer with the effective ferromagnetic Ising model on a simple square lattice. Magnetization and specific heat are investigated exactly at a field-driven phase transition from the singlet-dimer phase towards the fully saturated ferromagnetic phase, which changes from a discontinuous phase transition to a continuous one at a certain critical temperature. The mapping correspondence between the spin-1/2 Heisenberg FM/AF square bilayer and the ferromagnetic Ising square lattice suggests for this special critical point of the spin-1/2 Heisenberg FM/AF square bilayer critical exponents from the standard two-dimensional Ising universality class.     

Short-time dynamic behaviour of critical XY systems

Using Monte Carlo methods, the short-time dynamic scaling behaviour of two-dimensional critical XY systems is investigated. Our results for the XY model show that there exists universal scaling behaviour already in the short-time regime, but the values of the dynamic exponent z differ for different initial conditions. For the fully frustrated XY model, power law scaling behaviour is also observed in the short-time regime. However, a violation of the standard scaling relation between the exponents is detected.     

Nonasymptotic critical behaviour of uniaxial systems with strong dipolar interaction

Within a field-theoretic renormalization group approach general relations between specific heat, susceptibility and order parameter for uniaxial dipolar ferromagnets or ferroelectrics are derived. An advantage of these relations is that no explicit solution of the flow equation for the temperature dependence of the effective four-point coupling is needed. In this way the crossover from critical behaviour to mean field behaviour can be studied. The theory is applied to LiTbF₄ and TSCC.     

Critical behaviour of elastically coupled systems with spatially anisotropic critical fluctuations

The spatial anisotropy of critical fluctuations has strong influence on the temperature dependence of the elastic constants of an elastic medium coupled magneto- or electrostrictive to the order parameter. Under pinned boundary conditions we find for uniaxial dipolar systems of hexagonal and trigonal symmetry a second order phase transition, where only c₁₁ and c₁₂ show critical behaviour. For other symmetries a first order transition is expected. At an uniaxial Lifshitz point only c₃₃ becomes critical and the phase transition remains of second order for any symmetry.     

Two Kondo impurities in nanoscopic systems

We study the problem of two Kondo impurities in a small system. Using a slave boson approach we investigate the effect on the electron confinement of the Kondo physics of the two impurity problem. We show that the confinement splits the symmetric and antisymmetric channels and for small systems weakly coupled to a reservoir this gives two well defined behaviors: For the Fermi energy lying at a resonant state, the two impurities are Kondo screened with two characteristic energy scales. For the Fermi energy between two resonances, the inter-impurity interaction destroys the Kondo effect.Received: 2 February 2004, Published online: 28 May 2004PACS: 72.10.Fk Scattering by point defects, dislocations, surfaces, and other imperfections (including Kondo effect) - 72.15.Qm Scattering mechanisms and Kondo effect     

Dielectric critical behaviour at a metal-insulator transition under lattice compression

We study dielectric critical behaviour around a continuous metal-insulator transition in crystalline Cesium Iodide induced by changing the lattice parameter. The ab initio calculations of band structure and various quantities related to the dielectric response are performed in the transition region, within the local density approximation of the density functional theory. These calculations allow us to establish the power-law singularities of various quantities on two sides of the transition. The exponents obtained here are mean-field like due to the approximation in which interactions and disorder are treated. The critical behaviour is discussed by applying the scaling principle to the wavevector and frequency dependent dielectric function. We further investigate the effect of dielectric anomalies on optical properties by calculating the reflectance around transition region taking the ionic contribution to the dielectric function also into account. We find that the reflectance as a function of frequency shows very different kind of behaviour on both sides of the metal-insulator transition.     

Scaling behaviour of lattice animals at the upper critical dimension

We perform numerical simulations of the lattice-animal problem at the upper critical dimension d = 8 on hypercubic lattices in order to investigate logarithmic corrections to scaling there. Our stochastic sampling method is based on the pruned-enriched Rosenbluth method (PERM), appropriate to linear polymers, and yields high statistics with animals comprised of up to 8000 sites. We estimate both the partition sums (number of different animals) and the radii of gyration. We re-verify the Parisi-Sourlas prediction for the leading exponents and compare the logarithmic-correction exponents to two partially differing sets of predictions from the literature. Finally, we propose, and test, a new Parisi-Sourlas-type scaling relation appropriate for the logarithmic-correction exponents.     

Local polariton states in polar crystals with impurities

We show that an impurity embedded in an ionic crystal can give rise to a novel kind of local states. These states exist within a polariton gap of a material and are a mix of excitations of the crystal, such as phonons or excitons, and the transverse electromagnetic field. Electromagnetic components of the states along with the corresponding excitations of the material are localized in the vicinity of an impurity.