Infinite-order phase transition in a classical spin system

For an exactly soluble classical spin model with long-range inhomogeneous coupling it is proved that in the absence of external magnetic field the free energy is aC function of the temperature at the critical point.     

The projection operator approach to the Fokker-Planck equation. II. Dichotomic and nonlinear Gaussian noise

Two models for the Freedericksz transition in a fluctuating magnetic field are considered: one is based on a dichotomic and the other on a nonlinear Gaussian noise. Both noises are characterized by a finite correlation time. It is shown that the linear response assumption leading to the best Fokker-Planck approximation in the dichotomic and nonlinear Gaussian cases can be trusted only up to the order ¹ and ⁰, respectively. The role of the corrections to the linear response approximation is discussed and it is shown how to replace the non-Fokker-Planck terms stemming from these corrections with equivalent terms of standard type. This technique is shown to produce perfect agreement with the exact analytical results (dichotomic noise) and to satisfactorily fit the results of analog simulation (nonlinear Gaussian noise).     

Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.     

Spatial fluctuations in reaction-limited aggregation

A general method is used for describing reaction-diffusion systems, namely van Kampen's method of compounding moments, to study the spatial fluctuations in reaction-limited aggregation processes. The general formalism used here and in subsequent publications is developed. Then a particular model is considered that is of special interest, since it describes the occurrence of a phase transition (gelation). The corresponding rate constants for the reaction between two clusters of sizei and sizej areK _ij=ij (i, j=1, 2,). For thediffusion constants D _j of clusters of sizej the following class of models is considered:D _j=D if 1Js andD _j=0 ifj>s. The casess= ands< are studied separately. For the models= the equal-time and the two-time correlation functions are calculated; this modelbreaks down at the gel point. The breakdown is characterized by a divergence of the density fluctuations, and is caused by the large mobility of large clusters. For all models withs< the density fluctuations remain finite att _c, and the equal-time correlation functions in the pre- and in the post-gel stage are calculated. Many explicit and asymptotic results are given. From the exact solution the upper critical dimension in this gelling model isd _c=2.     

Ground state of a spin-phonon system. I. Variational estimates

A study is made of the ground-state energy of a spin-one-half particle in a fieldB and interacting with a phonon bath. The infrared-sensitive case of acoustic phonons with point coupling in three dimensions is characterized by two parameters, a coupling constant andB. Units are used where the high-momentum phonon cutoff is unity. There is a curve (B) separating a symmetry-breaking region with a long-range phonon field from a normal region. Two simple, well-known, approximations are compared. The source theory yields discontinuities in the first derivatives of the energy with respect toB and whenB>e ^–1 and an infinite-order transition whenB<e ^–1, but is trivial in the large- region. The classical theory yields discontinuities in the second derivatives but is trivial in the small- region. An improved variationally fixed ground-state wave function is analyzed. It gives a new (B) curve with an infinite-order transition with continuous energy derivatives whenB<e/(e ²–1/4) and with discontinuous derivatives whenB is larger than this value. It is nontrivial in the entire (B) plane. The crossover to classical behavior occurs near =1/2 forB1. But the wave function does not describe quantum fluctuations in the large- phase. A second way of combining source and classical effects is described. It yields a second-order transition (near =1/2 forB1) everywhere. These theories are special cases of a symmetry-breaking transformation together with a one-mode treatment of quantum fluctuations. The transition is viewed in terms of a single mode with a variable length, coupled dynamically to the spin.     

Formation of Amorphous AgI Aggregates Dominating Fast Ion Conductivity in AgI-based Glasses

Precise calorimetry was performed for (AgI)_x(AgPO₃)_1–x and (AgI)_x(Ag₂PO_3.5)_1–x glasses with very high AgI compositions (x0.75). The glasses showed -glass transitions due to the freezing-in of the rearrangement of conductive Ag⁺ ions. Magnitude of the associated heat-capacity jump increased with increasing the AgI composition in the respective glass systems, and was larger in the former system than in the latter when compared at the same AgI composition. All the results were well explained by the amorphous AgI aggregate model for the AgI-based fast ion conducting glasses, indicating the appropriateness of the model for the structure of the glasses with high AgI compositions. The formation of the hypothetical bulk amorphous AgI was also indicated in the glasses at the highest limit of AgI composition.This revised version was published online in November 2005 with corrections to the Cover Date.     

芳烃金属配合物在有机合成中的应用

本文讨论了芳烃金属配合物中的芳香部份在与金属配合后性质上的变化,以及这些变化后的性质在有机合成中的应用。     

过渡金属钼钒砷杂多化合物的合成与TPR,TPD研究

Seven transition metal molybdovanadoarsenic heteropoly compounds have been synthesized and characterized using IR, UV, TG-DTA, pH potential titration techniques. The molecular formulae of these compounds are pro-posed to be H_xM_yAsMO₁₀V₂O₄₀·zH₂O(x=1～3, y=1,2, M=Cr, Mn, Fe, Co, Ni, Cu, Zn).They are all keggin structure. Surface nature of these compounds have been investigated by temperature programmed desorption and temperature programmed reduction techniques. NH₃-TPD results show that in TPD profiles of the compounds there are two desorption peaks corresponding to weak acid sites of desorption, respectively. Desorbing activativon energy and preexponential factor of weak acid site of desorption for compounds have been calculated. H₂-TPR re-sults show that introducting transtion metal to molybdovanarsenic acid, the reduction peak temperatures of H₂-TPR shift regularly with increasing d electron numbers of transition metals. In addition, Zn and Cu heteropoly com-pounds have yet apparent effect of hydrogen spill over.     

Thermal coefficient of linear expansion of non-crystalline chalcogenides in the As-S-Se-Te-I system

The object of the paper is an investigation of the glasses of the (As₂S₃)_x(AsSe_0.5Te_0.5I)_100-x. type for 65≤;x≤;95, using methods of thermomechanical analysis. Values of the thermal coefficients of linear expansion in solid and visco-plastic phase were determined. it was shown that introducing arsenic-sulfide in glass-matrix AsChI, i.e. (AsSe_0.5Te_0.5I), leads to an increasing stability of these glasses. The characteristic temperatures of softening Tg and the temperature of the beginning of deformation t_w increase by increasing content of As₂S₃. The analytical forms of dependence of four significant physical values α_g, α_l, Tg, Tw, as a function of As₂S₃ content in the structure of glasses were fitted. This revised version was published online in July 2006 with corrections to the Cover Date.