On phase ordering behind the propagating front of a second-order transition

In a real system the heating is nonuniform, and a second-order phase transition to a broken-symmetry phase occurs by propagation of a temperature front. Two parameters, the cooling rate τ _Q and the transition front velocity ν _T determine the nucleation of topological defects. Depending on the relation of these parameters, two regimes are found: in the regime of fast propagation defects are created according to the Zurek scenario for the homogeneous case, while in the slow-propagation regime vortex formation is suppressed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 96–101 (10 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Optical sum rule in metals with strong electron-phonon interaction

The properties of a superconductor featuring strong electron-phonon and electron-impurity interactions have been studied in a single-band approximation. It is shown that the elastic scattering of electrons on static impurities decreases the electron-phonon interaction constant in proportion to the ratio of the electron-impurity relaxation rate and the seeding band width. The optical spectral weight (integral of the real part of the optical conductivity) in various energy intervals of a metal in the normal and superconducting states has been calculated as a function of the temperature and the superconducting gap. In the region of large (compared to the phonon) energies, the dependence of the spectral weight on the superconducting gap is weak, while the dependence on the temperature is completely determined by the corresponding dependence of the relaxation rate due to the elastic electron-phonon scattering far from the Fermi surface. It is shown that a difference in behavior of the spectral weight between the normal and superconducting states at lower energies is determined by so-called Holstein’s shift of the feature in the optical conductivity spectrum (rather than by the gap width, as it is commonly believed) and sharply decreases upon the introduction of impurities.     

Localized charge inhomogeneities and phase separation near a second-order phase transition

Localized charge inhomogeneities and phase separation are described in the framework of the phenomenological theory of phase transitions. It is shown that Coulomb interaction determines the charge distribution and the characteristic size of the emerging inhomogeneities. Phase separation associated with charge segregation becomes possible because of a high dielectric constant and a low excess charge density in the localization region. The phase diagram of the system is calculated, and estimates are obtained for the gain in energy associated with the emerging state. The role of Coulomb interaction is exposed, and corresponding estimates are given.     

Baryogenesis via density fluctuations with a second-order electroweak phase transition

We consider the presence of cosmic string-induced density fluctuations in the early universe at temperatures below the electroweak phase transition temperature. Resulting temperature fluctuations can restore the electroweak symmetry locally, depending on the amplitude of fluctuations and the background temperature. The symmetry will be spontaneously broken again in a given region as the temperature drops there (for fluctuations with length scales smaller than the horizon), resulting in the production of baryon asymmetry. The time-scale of the transition will be governed by the wavelength of fluctuation and, hence, can be much smaller than the Hubble time. This leads to strong enhancement in the production of baryon asymmetry for a second-order electroweak phase transition as compared to the case when transition happens due to the cooling of the universe via expansion. For a two-Higgs doublet model (with appropriate CP violation), we show that one can get the required baryon asymmetry if fluctuations propagate without getting significantly damped. If fluctuations are damped rapidly, then a volume factor suppresses the baryon production, though it is still 3–4 orders of magnitude larger than the conventional case of second-order transition.     

Threshold of oscillation in a ring-loop phase conjugator as a second-order optical phase transition

The threshold behavior is studied for a ring-loop coherent oscillator with a photorefractive strontium barium niobate (SBN) sample. A soft onset of oscillation is revealed and critical slowing down is observed in the temporal development of light-induced scattering below the threshold, thus pointing to a similarity with a second-order phase transition. Received: 10 July 2000 / Published online: 20 September 2000     

On a third-order phase transition

The asymptotic behaviour of random variables of the general form $$\ln \sum\limits_{i = 1}^{\kappa ^N } {\exp (N^{1/p} \beta \zeta _i )} $$ with independent identically distributed random variables ζ _i is studied. This generalizes the random energy model of Derrida. In the limitN→∞, there occurs a particular kind of phase transition, which does not incorporate a bifurcation phenomenon or symmetry breaking. The hypergeometric character of the problem (see definitions of Sect. 4), its Φ-function, and its entropy function are discussed.     

Effect of thermal phenomena on a second-order phase transition in the Landau-Ginzburg model

The influence of electrocaloric and pyroelectric effects on a phase transition in a ferroelectric material has been studied. The difference in the parameters of the Landau model for isothermal and adiabatic processes has been indicated. The temperature dependence of the spontaneous polarization is described by a special function (the probability integral) that results in the disappearance of the second-order phase transition.     

Symmetrization of the Coulomb pairing potential by electron-phonon interaction

It is shown that the Coulomb superconducting pairing in systems with the Fermi contour nesting can be described by a quasi-one-dimensional potential oscillating in real space. The supplement of this repulsive potential with an isotropic pairing attraction corresponding to the phonon superconductivity mechanism and including the effect of predominant forward scattering upon electron-phonon interaction leads to symmetrization of this potential and a considerable increase in the superconducting transition temperature.     

Adatom-adatom interaction mediated by an underlying surface phase transition

Low temperature scanning tunneling microscopy measurements on the adsorption of single Pb adatoms on Si(111)-(square root 3 x square root 3)-Pb surfaces reveal the vertical displacement patterns induced on the substrate by these Pb adatoms as well as a novel adatom-adatom interaction. The origin of both can be traced back to the (square root 3 x square root 3)<-->(3 x 3) phase transition taking place at lower temperatures. A Landau-like approach explains the displacement patterns as due to the corresponding order parameter and shows that the vicinity of a surface phase transition gives rise to a nonmonotonic adatom-adatom interaction.     

Magnetic relaxation in a spin-1 Ising model near the second-order phase transition point

The magnetic relaxation of a spin-1 Ising model with bilinear and biquadratic interactions is formulated within the framework of statistical equilibrium theory and the thermodynamics of irreversible processes. Using a molecular-field expression for the magnetic Gibbs energy, the magnetic Gibbs energy produced in the irreversible process is calculated and time derivatives of the dipolar and quadrupolar order parameters are treated as fluxes conjugate to their appropriate generalized forces in the sense of Onsager theory. The kinetic equations are obtained by introducing kinetic coefficients that satisfy the Onsager relation. By solving these equations an expression is derived for the dynamic or complex magnetic susceptibility. From the real and imaginary parts of this expression, magnetic dispersion and absorption factor are calculated and analyzed near the second-order phase transition.     

A second-order phase transition in the complete graph stochastic epidemic model

A stochastic model for epidemic spread in a set of individuals placed upon the sites of a complete graph of relations is investigated. The model is defined by three parameters: the number of individuals or sites, N, the probability that an infected site transmits the disease to a susceptible site, α, and the probability of recovery of infected sites, β, both referred to the unit of time.We show that this system evolves towards a, approximately Gaussian, stationary distribution of infected sites whose mean and variance can be analytically estimated. Also, we find that the average fraction of infected sites, x, is zero for transmission probabilities below the critical value α_c=1-e^-β/N and grows linearly with α for 0<α-α_c1. A sharp peak observed in Monte Carlo simulations of the variance of the number of infected sites as a function of α allows us to classify this dynamical phase transition as second order with x playing the role of an order parameter. Some consequences of this model to the dynamics of highly connected complex systems, such as the brain cortex, are also discussed.     

Anisotropic electron-phonon interaction in the cuprates

We explore manifestations of electron-phonon coupling on the electron spectral function for two phonon modes in the cuprates exhibiting strong renormalizations with temperature and doping. Applying simple symmetry considerations and kinematic constraints, we find that the out-of-plane, out-of-phase O buckling mode (B(1g)) involves small momentum transfers and couples strongly to electronic states near the antinode while the in-plane Cu-O breathing modes involve large momentum transfers and couples strongly to nodal electronic states. Band renormalization effects are found to be strongest in the superconducting state near the antinode, in full agreement with angle-resolved photoemission spectroscopy data.     

Elastic interaction between adatoms near a distortive phase transition

The indirect elastic interaction between two adatoms on substrates with a very small shear modulus such as V₃Si and Nb₃Sn near the transformation temperature T_M is calculated. As the temperature decreases towards T_M, the shear moduli of these materials go to zero, and the strength of the interaction increases dramatically. The interaction is strongly attractive if the adatoms are aligned along a cube axis and repulsive if they are at 45° to the axis.     

On the gas-liquid phase transition

A new approach to the problem of the gas-liquid phase transition, based on the Mayer cluster expansion of the partition function, is proposed. It is shown that the necessary and sufficient condition for phase transition to occur is that there exist a temperatureT= T_c > 0 such that forT T _c, all theb _l (except perhaps a finite number of them) are positive, where theb _l, are the cluster integrals (as defined by Mayer) in the thermodynamic limit. Explicit expressions for the isotherms for gas-saturated vapor and liquid phases are given.     

Unambiguous determining the Curie point in perovskite manganite with second-order phase transition by scaling method

The accurate determination of the Curie temperature (T_C) is particularly important in describing the magnetic behavior close to the paramagnetic-ferromagnetic (PM-FM) phase transition. In this paper, we studied the magnetic phase transition and accurately predicted the Curie point of perovskite manganite La_0.825Sr_0.175MnO₃. We find the compound shows a second-order PM-FM transition and has a large magnetic entropy change (MEC) in vicinity of phase transition region. Based on the scaling law and the correlation between magnetic field and MEC, the precise and magnetic-independent Curie temperature was determined to be 281.7 K, obviously lower than 285.4 K decided from the magnetization versus temperature. The reliability of new Curie temperature can be well confirmed by the modified Arrott plot together with the critical exponents. Our results not only open up a new pathway for precise definition of Curie point but also facilitate the efficient exploitation of spontaneous magnetic bubbles in perovskite manganite.     

On the possibility of superconductive transition in a strong magnetic field

The possible existence of triplet superconductive transition in metals in a strong magnetic field is shown. In such system in the sufficiently strong magnetic field there are no currents, which can destroy the superconductivity.