Critical line near the zero-density critical point of the Kosterlitz-Thouless transition

Using low-fugacity expansions, we study the exact behavior of the Kosterlitz-Thouless critical line near the zero-density critical point. We show that the critical temperature deviates from its zero-density value by a term proportional to the square root of the density.     

Correlations in the Kosterlitz-Thouless phase of the two-dimensional Coulomb gas

The particle and charge correlations of the two-dimensional Coulomb gas are studied in the dielectric phase. A term-by-term analysis of the low-fugacity expansions suggests that the large-distance behaviors of the particle correlations are governed by multipolar interactions, similar to what happens in a system of permanent dipoles. These behaviors are compatible with the asymptotic structure of the BGY hierarchy equations; on the other hand, a new identity for the dielectric constant is used to show that the four-particle correlations decay as the dipole-dipole potential 1/r² when two neutral pairs are separated by a large distancer. Near the zero-density critical point of the Kosterlitz-Thouless transition, we resum the low-fugacity expansions of both 1/ and the charge correlation C(r). We thus retrieve the coupling constant flow equations of the renormalization group as well as the effective interaction energy of the iterated mean-field theory by Kosterlitz and Thouless. The coupling constant at the RG fixed point is then identified with 1/. The nonanalyticity of 1/ at the transition turns out to coincide with the divergence of the low-fugacity series for this quantity. The leading term in the large-distance behavior of C(r) is found to be the same as for external charges. Moreover, we exhibit the subleading terms which also contribute to 1/.     

A new rigorous upper bound for the inverse critical temperature of the two-dimensional Coulomb gas

In this paper we show how to improve the recent result _c 17.2 on the inverse critical temperature for the two-dimensional Coulomb gas at low density to get the following upper bound: _c 16.     

Mean-field kinetic theory of a classical electron gas in a periodic potential. I. Formal solution of the Vlasov equation

We study the static and dynamic behavior of a classical electron gas in the periodic potential created by an ionic lattice. Using the well-known Vlasov approximation, we derive a mean-field kinetic equation for the density-response function of the electrons. This equation is formally solved in terms of the trajectories of one electron in the mean-field equilibrium potential which determines the local electronic density. The mean-field expressions of the static and dynamic structure factors are then obtained through the fluctuation-dissipation theorem. These expressions are used to show that within the mean-field approximation the system is a conductor at all temperatures and for all dimensions.     

On the statistical mechanics of classical Coulomb and dipole gases

A detailed, rigorous study of the statistical mechanics-screening- and critical properties, phase diagrams, etc., of classical Coulomb monopole and dipole gases in two or more dimensions is presented. The statistical mechanics of the two-dimensionalXY and Villain models is reconsidered and related to the one of two-dimensional lattice Coulomb gases. At low temperatures and moderate densities those gases behave like dipole gases. The Kosterlitz-Thouless transition is analyzed in that perspective and characterized by an order parameter. Techniques useful for a proof of existence of such a transition in a two-dimensional hard-core Coulomb gas are developed and applied to the study of dipole gases.A Sloan Fellow, and supported in part by NSF grant No. DMR 7904355.     

A testbench for the nested dipole hypothesis of Kosterlitz and Thouless

We consider the two-dimensional one-component plasma without a background and confined to a half-plane near a metal wall. The particles are also subjected to an external potential acting perpendicular to the wall with an inverse-power-law Boltzmann factor. The model has a known solvable isotherm which exhibits a Kosterlitz-Thouless-type transition from a conductive to an insulator phase as the power law is varied. This allows predictions of theoretical methods of analyzing the Kosterlitz-Thouless transition to be compared with the exact solution. In particular, we calculate the asymptotic density profile by resumming its low-fugacity expansion near the zero-density critical coupling in the insulator phase, and solving a mean-field equation deduced from the first BGY equation. Agreement with the exact solution is obtained. As the former calculation makes essential use of the nested dipole hypothesis of Kosterlitz and Thouless, the validity of this hypothesis is explicitly verified.     

Relations between the Coulomb gas picture and conformal invariance of two-dimensional critical models

Partition functions of critical 2D models on a torus can be derived from their microscopic formulation and their free field representation in the continuum limit. This is worked out explicitly for theO(n) andQ-state Potts model. Forn orQ integer we recover results obtained from conformal invariance, but our procedure also extends to nonintegral values. In the latter case the expansion on characters of the Virasoro algebra involves real coefficients of either sign. The operator content of both models is discussed in detail.     

On the absence of intermediate phases in the two-dimensional Coulomb gas

For a simple, continuum two-dimensional Coulomb gas (with soft cutoff), Gallavotti and Nicoló [J. Stat. Phys. 38:133–156 (1985)] have proved the existence of finite coefficients in the Mayer activity expansion up to order 2n below a series of temperature thresholdsT _n =T [1+(2n–1)^–1] (n=1, 2,...). With this in mind they conjectured that an infinite sequence of intermediate, multipole phases appears between the exponentially screened plasma phase aboveT ₁ and the full, unscreened Kosterilitz-Thouless phase belowT T _KT. We demonstrate that Debye-Hückel-Bjerrum theory, as recently investigated ford=2 dimensions, provides a natural and quite probably correct explanation of the pattern of finite Mayer coefficients while indicating the totalabsence of any intermediate phases at nonzero density ; only the KT phase extends to >0.     

Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas

Many two-dimensional spin models can be transformed into Coulomb-gas systems in which charges interact via logarithmic potentials. For some models, such as the eight-vertex model and the Ashkin-Teller model, the Coulomb-gas representation has added significantly to the insight in the phase transitions. For other models, notably theXY model and the clock models, the equivalence has been instrumental for almost our entire understanding of the critical behavior. Recently it was shown that theq-state Potts model and then-vector model are equivalent to a Coulomb gas with an asymmetry between positive and negative charges. Fieldlike operators in these spin models transform noninteger charges and magnetic monopoles. With the aid of exactly solved models the Coulombgas representation allows analytic calculation of some critical indices.     

万亿摄氏度下烹煮夸克汤：核物质相结构和量子色动力学相变临界点的实验研究

高温高密核物质相结构是核物理研究领域的热点和前沿。量子色动力学(QCD)相变临界点的实验确认将是探索核物质相结构的里程碑,具有重要科学意义。为了在这一具有潜在重大发现的研究方向上占据领先地位、取得突破,各国纷纷建造大型加速器以及粒子探测器,开展重离子碰撞实验,其主要目标就是从实验上探索高温高密核物质相结构、寻找QCD相变临界点。文章总结了近年来相对论重离子碰撞中核物质相结构及QCD临界点的实验研究进展,并对未来探索高重子密度区核物质相结构、寻找QCD临界点的重要实验装置做了展望。     

The microstructure and Ruppeiner geometry of charged anti-de Sitter black holes in Gauss–Bonnet gravity: from the critical point to the triple point

Ruppeiner geometry has been successfully applied in the study of the black hole microstructure by combining with the small–large black hole phase transition, and the potential interactions among the molecular-like constituent degrees of freedom are uncovered. In this paper, we will extend the study to the triple point, where three black hole phases coexist acting as a typical feature of black hole systems quite different from the small–large black hole phase transition. For the six-dimensional charged Gauss–Bonnet anti-de Sitter black hole, we thoroughly investigate the swallow tail behaviors of the Gibbs free energy and the equal area laws. After obtaining the black hole triple point in a complete parameter space, we exhibit its phase structures both in the pressure–temperature and temperature–horizon radius diagrams. Quite different from the liquid–vapor phase transition, a double peak behavior is present in the temperature–horizon radius phase diagram. Then we construct the Ruppeiner geometry and calculate the corresponding normalized curvature scalar. Near the triple point, we observe multiple negatively divergent behaviors. Positive curvature scalar is observed for the small black hole with high temperature, which indicates that the repulsive interaction dominates among the microstructure. Furthermore, we consider the variation of the curvature scalar along the coexisting intermediate and large black hole curves. Combining with the observation for different fluids, the result suggests that this black hole system behaves more like the argon or methane. Our study provides a first and preliminary step towards understanding black hole microstructure near the triple point, as well as uncovering the particular properties of the Gauss–Bonnet gravity.     

The 2D Rancieite-type manganic acid and its alkali-exchanged derivatives: Part I — Chemical characterization and thermal behavior

The 2D Rancieite type manganic acid was prepared by reduction of KMnO₄ in acidic medium. Its ion exchange behavior allows to prepare alkali derivatives. All compounds were characterized with use of a combination of X-ray diffraction, chemical analyses, TGA, magnetic measurements and spectroscopic techniques. The evolution of their chemical composition versus temperature was studied between 180 and 400 °C. It shows that the dehydration process is partly reversible in these compounds whereas the weak reduction is irreversible. The 2D Rancieite-type manganic acid is readily different from a Birnessite-type phyllomanganate, as shown by several features: the interlayer distance, the ion exchange capacity, the thermal behavior, the interlayer cation content, the manganese average oxidation state, the magnetic behavior and the IR spectrum.     

The Uses of Polynuclear Metal Complexes to Develop Designed Dispersions of Supported Metal Oxides: Part I. Synthesis and Characterization

One way to design a catalyst begins with a consideration of thereaction mechanism to the desired product so that only the chemistryrequired of that mechanism will be present on the surface. The reactionmechanism will suggest the structure(s) to be developed on the surface whichshould be stabilized against changes during operation. We believe that thisideal may be approached by decorating surfaces or porous powders with amonolayer of metal complexes having the desired structures. These complexesmay be partially decomposed to develop a high dispersion of the supportedmetal oxide.     

Comparative analysis of purely classical and semiclassical approaches to collision line broadening of polyatomic molecules: I. C2H2-Ar case

Semiclassical approaches to the computation of spectral line parameters stay up to nowadays one of the working tools complementary to refined but costly quantum-mechanical methods. Using of the trajectory concept together with quantum treatment of internal molecular motions imposes however the hypothesis of rotation-translation decoupling and translational motion governed by the isotropic potential. When a posteori justified for small heavy colliders, this hypothesis appears as doubtful for long polyatomic molecules. At the same time, purely classical methods, even requiring the artificial procedure of the correspondence principle with quantum mechanics, easily take into account the rototranslational energy transfer through the trajectory governed by the full anisotropic potential. The infrared line broadening of a typically classical C₂H₂-Ar system at various temperatures is analyzed here from these two different points of view. When a refined ab initio potential is chosen to represent the interaction energy, the semiclassical approach leads to a visible overestimation of the line broadening for all values of the rotational quantum number and for all temperatures studied whereas the fully classical treatment gives a quite satisfactory prediction. These fully classical computations show that even for C₂H₂-Ar the rototranslational coupling is quite important, and variations of the translational motion parameters during collisions produce detectable changes in rotation. When, for the sake of a meaningful comparison with the semiclassical approach, the isotropic trajectories are imposed within the classical method, this leads to smaller line widths; the effect strongly depends, however, on the peculiarities of potential energy surface, temperature, and rotational quantum number value.     

On the accuracy of classical, semiclassical and quantum methods in collision line broadening calculations: Comparative analysis for C2H2-Ar, He systems

Accuracies of classical, semiclassical and quantum methods are comprehensively examined in calculations of impact line widths of C₂H₂ molecules perturbed by Ar and He. The field of comparative study covers both infrared absorption and Raman scattering lines of acetylene having rotational quantum number J=0-30 at temperatures 173 and 296 K. Calculations have been made by fully classical method and by three basic least approximate semiclassical methods, namely, Neilsen-Gordon (NG) method, peaking approximation (PA) and Smith-Giraud-Cooper (SGC) method. Most accurate ab initio potential energy surfaces (PES) of Yang et al. (1996) [21] and Mozsynski et al. (1995) [22] have been applied to model C₂H₂-Ar and C₂H₂-He interactions. The comparison has been made also with available experimental data and with the results of rigorous fully quantum-mechanical calculations within close coupling and coupled states approaches in identical conditions. Semiclassical methods are proved to be not so much accurate as it is generally believed since all they gave in the cases considered seriously underestimated results. The fundamental issue of the adequacy of simplified trajectories in collision broadening calculations is finally reasonably solved. In cases of C₂H₂-Ar and C₂H₂-He systems the use of the “exact” isotropic trajectories (i.e. driven only by the isotropic part of PES) is the main reason of failing of NG, PA and SGC methods. Thus the neglecting of back-influence of the RT exchange on the classical path is a principal defect of semiclassical methods. Finally, the application of simplified trajectories is recognized as inadequate and risky in broadening calculations for molecules having relatively small rotational constants when accurate ab initio PES are applied.     

The 2‐matrix of the spin‐polarized electron gas: contraction sum rules and spectral resolutions

The spin‐polarized homogeneous electron gas with densities ρ_↑ and ρ_↓ for electrons with spin ‘up’ (↑) and spin ‘down’ (↓), respectively, is systematically analyzed with respect to its lowest‐order reduced densities and density matrices and their mutual relations. The three 2‐body reduced density matrices γ_↑↑, γ_↓↓, γ_a are 4‐point functions for electron pairs with spins ↑↑, ↓↓, and antiparallel, respectively. From them, three functions G_↑↑(x,y), G_↓↓(x,y), G_a(x,y), depending on only two variables, are derived. These functions contain not only the pair densities according to g_↑↑(r) = G_↑uarr;(0,r), g_↓↓(r) = G_↓↓(0,r), g_a(r) = G_a(0,r) with r = | r ₁ ‐ r ₂|, but also the 1‐body reduced density matrices γ_↑ and γ_↓ being 2‐point functions according to γ_s = ρ_sf_s and f_s(r) = G_ss(r, ∞) with s = ↑,↓ and r = | r ₁ ‐ r ^′₁|. The contraction properties of the 2‐body reduced density matrices lead to three sum rules to be obeyed by the three key functions G_ss, G_a. These contraction sum rules contain corresponding normalization sum rules as special cases. The momentum distributions n_↑(k) and n_↓(k), following from f_↑(r) and f_↓(r) by Fourier transform, are correctly normalized through f_s(0) = 1. In addition to the non‐negativity conditions n_s(k),g_ss(r),g_a(r) ≥ 0 [these quantities are probabilities], it holds n_s(k) ≤ 1 and g_ss(0) = 0 due to the Pauli principle and g_a(0) ≤ 1 due to the Coulomb repulsion. Recent parametrizations of the pair densities of the spin‐unpolarized homogeneous electron gas in terms of 2‐body wave functions (geminals) and corresponding occupancies are generalized (i) to the spin‐polarized case and (ii) to the 2‐body reduced density matrix giving thus its spectral resolutions.     

The determination of the true profile of XPS line by regularization method: I. Mathematical algorithm and numerical simulations

The resolution of XPS spectra is limited mainly by instrumental parameters like the spectral line width of exciting X-ray source and the finite energy resolution of the electron analyzer. A new algorithm of an inverse ill-posed problem has been proposed in which low resolution experimental XPS data can be enhanced by removing the instrumental functions. The regularization method with a special fast iteration algorithm is applied for determining the true profile line of a complex chemical compound if we know excitation and instrumental functions. This paper is structured as follows: (I) a mathematical algorithm is described and numerical simulation results are presented. (II) These algorithms have been applied to the poorly resolved C 1s spectrum of a poly-methyl methacrylate (PMMA) film studied by the conventional technique with monochromatic and polychromatic radiation. The resulting enhancement allows previously unresolved structure to be observed without any assumptions concerning number, position, shape of peaks and their ratio.     

A multispectrum analysis of the ν2 band of HCN: Part I. Intensities, broadening, and shift coefficients

Absolute intensities, self- and air-broadening coefficients, self- and air-induced shift coefficients and their temperature dependences have been determined for lines belonging to the P- and R-branches of the ν₂ band of H¹²C¹⁴N centered near 712 cm⁻¹. Infrared spectra of HCN in the 14-μm region were obtained at high resolution (0.002-0.008 cm⁻¹) using two different Fourier transform spectrometers (FTS), the McMath-Pierce FTS at the National Solar Observatory on Kitt Peak and the Bruker IFS 120HR FTS at the Pacific Northwest National Laboratory. Spectra were recorded with 99.8% pure HCN as well as lean mixtures of HCN in air at various temperatures ranging between +26 and −60 °C. A multispectrum nonlinear least squares technique was used to fit selected intervals of 36 spectra simultaneously to obtain the line positions, intensities, broadening, and shift parameters. The measured line intensities were analyzed to determine the vibrational band intensity and the Herman-Wallis coefficients. The measured self-broadening coefficients vary between 0.2 and 1.2 cm⁻¹ atm⁻¹ at 296 K, and the air-broadening coefficients range from 0.08 to 0.14 cm⁻¹ atm⁻¹ at 296 K. The temperature dependence exponents of self-broadening range from 1.46 to −0.12 while the corresponding exponents for air broadening vary between 0.58 and 0.86. The present measurements are the first known determination of negative values for the temperature dependence exponents of HCN-broadening coefficients. We were able to support our self-broadening measurements with appropriate theoretical calculations. Our present measurements are compared, where possible, with previous measurements for this and other HCN bands, as well as the parameters that are included in the 2000 and 2004 editions of the high-resolution transmission (HITRAN) database.