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.     

Critical behavior of heat capacity of the SC(NH2)2 ferroelectric in the region of incommensurate phase transition

The anomalous (nonclassical) behavior of heat capacity in the region of the second-order phase transition “initial phase-incommensurate phase” was experimentally observed in the SC(NH₂)₂ ferroelectric. Such a critical behavior of heat capacity above and below the temperature of incommensurate phase transition is shown to be qualitatively consistent with the fluctuation theory of XY-type systems.     

Ordering potential: the anomalous structure and properties of liquid KPb alloy

The anomalous structure and related properties of liquid KPb alloy are presented through an ab initio evaluated ordering potential as a function of concentration. It appears that considerable ordering occurs and it maximizes at the stoichiometric composition (c_k∼0.5). We then use the model to obtain the Bhatia-Thornton(BT) structure factors at different compositions (c_k=0.1,0.3,0.5 and 0.8). The calculations of concentration fluctuation and other related thermodynamic properties show that this ordering potential approach works reasonably for this compound forming liquid alloy.     

Birth of a New Class of Period-Doubling Scaling Behavior as a Result of Bifurcation in the Renormalization Equation

It is found that a fixed point of the renormalization group equation corresponding to a system of a unimodal map with extremum of power κ and a map summarizing values of a function of the dynamical variable of the first subsystem, undergoes a bifurcation in the course of increase of κ. It occurs at κ _c =1.984396 and results in a birth of the period-2 stationary solution of the RG equation. At κ=2 this period-2 solution corresponds to the universal period-doubling behavior discovered earlier and denoted as the C-type criticality (Kuznetsov and Sataev in Phys. Lett. A 162:236–242, 1992). By combination of analytical methods and numerical computations we obtain and analyze an asymptotic expansion of the period-2 solution in powers of Δκ=κ−κ _c . The developed approach resembles the ε-expansion in the phase transition theory, in which a “trivial” stationary point of the RG transformation undergoes a bifurcation that gives rise to a new fixed point responsible for the critical behavior with nontrivial critical indices.     

Phase transitions in “small” systems

Traditionally, phase transitions are defined in the thermodynamic limit only. We discuss how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be seen and classified for small systems. “Small” systems are systems where the linear dimension is of the characteristic range of the interaction between the particles; i.e. also astrophysical systems are “small” in this sense. Boltzmann defines the entropy as the logarithm of the area of the surface in the mechanical N-body phase space at total energy E. The topology of S(E,N) or more precisely, of the curvature determinant allows the classification of phase transitions without taking the thermodynamic limit. Micro-canonical thermo-statistics and phase transitions will be discussed here for a system coupled by short range forces in another situation where entropy is not extensive. The first calculation of the entire entropy surface S(E,N) for the diluted Potts model (ordinary (q=3)-Potts model plus vacancies) on a square lattice is shown. The regions in {E,N} where D>0 correspond to pure phases, ordered resp. disordered, and D<0 represent transitions of first order with phase separation and “surface tension”. These regions are bordered by a line with D=0. A line of continuous transitions starts at the critical point of the ordinary (q=3)-Potts model and runs down to a branching point P_m. Along this line vanishes in the direction of the eigenvector of D with the largest eigen-value . It characterizes a maximum of the largest eigenvalue . This corresponds to a critical line where the transition is continuous and the surface tension disappears. Here the neighboring phases are indistinguishable. The region where two or more lines with D=0 cross is the region of the (multi)-critical point. The micro-canonical ensemble allows to put these phenomena entirely on the level of mechanics. Received 18 October 1999 and received in final form 17 November 1999     

Local structural order and single-particle dynamics in metallic glass

The atomic dynamics of the amorphous metallic alloy Al₅₀Cu₅₀ is investigated in this work. The critical glass-forming temperature is defined from the behavior change of the Wendt—Abraham parameter and the pair-correlation entropy, and is T _c ≈ 500 K. It is shown that the power-fractional memory function allows us to describe in the framework of the mode-coupling theory the time dependences of the incoherent scattering functions obtained from the atomic dynamic simulations for the wide region of temperatures (T = 100–2000 K).     

Asymptotic Behavior of the Magnetization Near Critical and Tricritical Points via Ginzburg–Landau Polynomials

The purpose of this paper is to prove connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials that we call the Ginzburg–Landau polynomials. The model under study is a mean-field version of a lattice spin model due to Blume and Capel. It is defined by a probability distribution that depends on the parameters β and K, which represent, respectively, the inverse temperature and the interaction strength. Our main focus is on the asymptotic behavior of the magnetization m(β _n ,K _n ) for appropriate sequences (β _n ,K _n ) that converge to a second-order point or to the tricritical point of the model and that lie inside various subsets of the phase-coexistence region. The main result states that as (β _n ,K _n ) converges to one of these points (β,K), . In this formula γ is a positive constant, and is the unique positive, global minimum point of a certain polynomial g. We call g the Ginzburg–Landau polynomial because of its close connection with the Ginzburg–Landau phenomenology of critical phenomena. For each sequence the structure of the set of global minimum points of the associated Ginzburg–Landau polynomial mirrors the structure of the set of global minimum points of the free-energy functional in the region through which (β _n ,K _n ) passes and thus reflects the phase-transition structure of the model in that region. This paper makes rigorous the predictions of the Ginzburg–Landau phenomenology of critical phenomena and the tricritical scaling theory for the mean-field Blume–Capel model.     

Metal-insulator transition in amorphous Si1−c Mnc obtained by ion implantation

A metal-insulator transition (MIT) induced by a change in the impurity Mn concentration in a material with topological disorder — amorphous Si_1−c Mn_c — is investigated. It is found that near the critical point the localization radius, permittivity, and conductivity vary according to a power law in accordance with the scaling theory of localization. The critical exponents are determined. It is concluded that the basic mechanisms of the MIT in disordered systems do not depend on the type of disorder and are universal. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 4, 333–337 (25 February 1997)     

Random Walks and Polymers in the Presence of Quenched Disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both ‘random walk models’, where the random walk is a dynamical process generated by local transition rules, and on ‘polymer models’, where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points: thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures T _c(i,L) over the ensemble of samples (i) of size L. We describe the results of this analysis for the bidimensional wetting and for the Poland–Scheraga model of DNA denaturation.Conference Proceedings “Mathematics and Physics”, I.H.E.S., France, November 2005     

Spin fluctuations and high temperature superconductivity

Theory of spin fluctuations for itinerant magnetism and its application to high temperature superconductivity are reviewed. After a brief introduction to the whole subject the developments of the self-consistent renormalization theory of spin fluctuations are summarized with particular emphasis on critical properties at the quantum phase transitions. Most of the anomalous properties in the normal state of high-T_c cuprates are understood as due to the critical behaviours for the two dimensional antiferromagnetic metals. By analysing the nuclear magnetic relaxation rate and the T-linear term of resistivity, the set of parameters to specify the spin fluctuations are determined. It is shown that by using the parameters thus obtained one can describe other quantities as well, e.g. optical conductivity. Then we proceed to the theory of superconductivity by the spin fluctuation mechanism. After some discussion on the weak coupling treatments, the strong coupling theory is reviewed. It is shown that the set of parameters determined by the normal state properties of the high-T _c cuprates just give a transition temperature of the right order of magnitude. Among the parameters, the most sensitive one for T _c is the frequency spread of the spin fluctuations. This fact enables us to present a possible unified picture of the antiferromagnetic spin fluctuation-induced superconductors, including heavy fermion superconductors and organic superconductors. This point of view may be confirmed to a certain extent by microscopic calculations based on the fluctuation exchange approximation for the two-dimensional Hubbard models representing not only the cuprates but also organic and trellis lattice compounds. The review is concluded with some discussions on future problems, e.g. the pseudo spin-gap in the under-doped region.     

Depolarized light scattering in a 2.6-lutidine-water solution near the critical point

The spectra of depolarized Rayleigh light scattering, i.e., the Rayleigh line wing (RLW), and Raman scattering in a solution with the lower critical point in the phase separation diagram is experimentally studied. The Rayleigh line wing is studied to 30 cm^?1 from the exciting light frequency; the Raman scattering line (RSL) is studied in the near profile region. In the vicinity of the lower critical point, as well as in solutions with the upper critical point, strong narrowing of the RLW and RSL is observed. In this case, the conditions arise for the manifestation of the profile in the Rayleigh line spectrum, which is caused by the interaction of concentration and anisotropy fluctuations. Previously, this spectral line was theoretically predicted by I. A. Chaban in [1].     

Anomalous light-induced drift of lithium atoms in a mixture of noble gases

This paper is a theoretical study of the spectral features of the velocity of light-induced drift (LID) of lithium atoms (⁷Li and ⁶Li) in a binary mixture of noble gases: Ne + Ar, Ne + Kr, and Ne + Xe. The spectral shape of the LID signal is predicted to depend strongly on the fraction ξ of neon in the buffer mixture in the range ξ≈0.8–0.9 (ξ=N _Ne/N _b, where N _Ne is the neon concentration, and N _b is the total concentration of the buffer particles). When the velocity of anomalous LID is treated as a function of the radiation frequency, it is found to have one, three, five, or seven zeros and to differ substantially from the dispersion-curve-like behavior with one zero predicted by the standard LID theory with velocity-independent transport collision rates. The reason for these additional zeros of the drift velocity is the alternating-sign dependence on the lithium-atom velocity of the relative difference of transport rates of collisions between buffer particles and excited and unexcited atoms. What is also established is that the anomalous LID of lithium atoms can be observed at almost all temperatures, depending on the value of ξ. At a fixed temperature, anomalous LID can be observed only in a narrow range of values of the fraction of neon in the buffer mixture, Δξ≈0.02. The results make possible highly precise testing in the LID experiments of the interatomic potentials used in calculations of the velocity spectrum of anomalous LID. Zh. éksp. Teor. Fiz. 116, 1587–1600 (November 1999)     

两种扩展Harper模型的波包动力学

本文通过二次矩M₂(t)和概率分布W_n(t)数值地研究了两种扩展Harper模型的波包动力学,得到了这两种模型中各个相、各条临界线以及三相点的波包扩散情况.对于第一种扩展Harper模型,发现两个金属相中波包是弹道扩散的,在绝缘体相中波包不扩散,而在三相点以及各条临界线上波包是反常扩散的.同时,发现金属相—金属相转变的临界线上的波包动力学行为与金属相—绝缘体相转变的临界线上的相同,但三相点的动力学行为与各临 关键词： 金属绝缘体转变 扩展Harper模型 波包动力学     

Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method

The values of the insulator gap Δ in one-dimensional systems of interacting bosons described by the Hubbard Hamiltonian are calculated at low temperatures by the quantum world-line Monte Carlo algorithm. The dependence of Δ on the size of the system, the temperature, and the parameters of the model is investigated. It is shown that a chain with N _a=50 sites is already sufficient to estimate the thermodynamic value of the critical quantity (t/U)_c for which a transition from the insulator into the superfluid state occurs in a commensurate system. To within the computational error, this value, (t/U)_c=0.300±0.005, agrees with the value (t/U)_c=0.304±0.002 obtained previously by the combined “exact diagonalization + renormalization-group analysis” method. The characteristic Kosterlitz-Thouless behavior of the insulator gap is demonstrated near the critical region: Δ∼exp[−b(1−t/t _c)^−1/2]. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 92–96 (25 July 1996)     

Lattice dynamics and structural phase transitions

Results of lattice dynamics, or atomic motions in a solid, explain many of the thermodynamic properties of solids. Inelastic neutron scattering conveniently explores the atomic motions, quantized as phonons. Of particular interest are materials that undergo structural phase transitions. The soft mode theory has been successful in relating anomalous phonon behavior to structural changes in solids. One such example is the ferromagnetic shape memory alloy, Ni₂MnGa, which undergoes a sequence of phase transitions leading to a magnetic, incommensurate modulated, tetragonal phase as the ground state. The experiments, coupled with first principles calculations, provide evidence that strong electron–phonon coupling is the driving mechanism of the phase transformation.     

Bulk singularities at critical end points: a field-theory analysis

A class of continuum models with a critical end point is considered whose Hamiltonian [φ,ψ] involves two densities: a primary order-parameter field, φ, and a secondary (noncritical) one, ψ. Field-theoretic methods (renormalization group results in conjunction with functional methods) are used to give a systematic derivation of singularities occurring at critical end points. Specifically, the thermal singularity ∼ | t|^{2 - α} of the first-order line on which the disordered or ordered phase coexists with the noncritical spectator phase, and the coexistence singularity ∼ | t|^{1 - α} or ∼ | t|^β of the secondary density <ψ> are derived. It is clarified how the renormalization group (RG) scenario found in position-space RG calculations, in which the critical end point and the critical line are mapped onto two separate fixed points _CEP ^* and _λ ^*, translates into field theory. The critical RG eigenexponents of _CEP ^* and _λ ^* are shown to match. _CEP ^* is demonstrated to have a discontinuity eigenperturbation (with eigenvalue y = d), tangent to the unstable trajectory that emanates from _CEP ^* and leads to _λ ^*. The nature and origin of this eigenperturbation as well as the role redundant operators play are elucidated. The results validate that the critical behavior at the end point is the same as on the critical line. Received 18 January 2001     

Kinetic theory of fluctuations near a convective instability

The kinetic theory of density and velocity fluctuations below and above the first convective instability in a Benard cell is presented. Results are given in a form valid for all fluid densities. In particular, the singular behavior near the instability point is computed and a detailed comparison with that near a critical point is made. Mode coupling effects, involving the viscous and the heat mode, that determine the singular behavior of the thermal conductivity near the critical point, are also responsible for the singular behavior of the pair correlation function and in particular the density-density correlation function near the instability point. The anomalous density fluctuations could be measured directly by microwave scattering experiments, while the velocity fluctuation could be measured by laser Doppler velocimetry.     

The effect of thermodynamic fluctuations on the formation of superstructures in random heteropolymers

The behavior of a random AB block copolymer with the same fraction of monomers of each type near the critical point has been studied. In the Brazovskii approximation it is shown that thermodynamic fluctuations give rise to a lamellar structure whose period is greater than the size of a block. The structure appears as a result of a first-order phase transition. The parameters of this transition are calculated and the region of coexistence of the disordered and lamellar phases is found. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 3, 183–187 (10 August 1996)     

Ionic contribution to Rayleigh line wing under conditions of light scattering by liquid electrolytic solutions

A theoretical treatment is performed of the mechanism (suggested in N. F. Bunkin andA. V. Lobeev, Z. Phys. Chem. 214, 269 (2000)) of ionic effect on the Rayleigh line wing under conditions of light scattering by liquid electrolytic solutions. The mechanism consists essentially in that the fluctuation electric field caused by Brownian motion of ions dissolved in a liquid leads, because of the Kerr polarization effect, to fluctuations of optical anisotropy of the scattering medium. The spectral characteristics of the Rayleigh line wing are obtained using the fluctuation-dissipative theorem as applied to equilibrium thermal electromagnetic field. Expressions are derived for the integral intensity and spectral width (Δν) of the Rayleigh line wing in terms of parameters of liquid solution such as the temperature T, the viscosity η, the concentration of dissolved ions n _i, and the coefficient of their diffusion D _i. It is demonstrated that Δν ∝ exp(?W/2T), where W is the activation energy of ion mobility b _i = D_i/T. The possible region of validity of developed theoretical concepts as applied to the experimental data for the Rayleigh line wing in electrolytic solutions is discussed.     

Calorimetric studies of C70S48 crystals

A comparative study of the thermodynamic properties of the C₇₀ fullerene, sulfur, and C₇₀S₄₈ crystals has been made by differential scanning calorimetry. It is shown that only C₇₀S₄₈ has an endothermic δ phase transition with a peak at 430 K, which lies in the temperature region exhibiting conductivity and dielectric anomalies. A correlation between the behavior of the sulfur sublattice in the C₇₀S₄₈ crystals and the thermodynamic parameters of the transition has been established. Fiz. Tverd. Tela (St. Petersburg) 41, 360–363 (February 1999)