XXZ Spin Chain with the Asymmetry Parameter Δ = −1/2: Evaluation of the Simplest Correlators

We consider a finite XXZ spin chain with periodic boundary conditions and an odd number of sites. It appears that for the special value of the asymmetry parameter = –1/2, the ground state of this system described by the Hamiltonian has the energy E ₀ = –3N/2. Although the ground state is antiferromagnetic, we can find the corresponding solution of the Bethe equations. Specifically, we can explicitly construct a trigonometric polynomial Q(u) of degree n = (N–1)/2, whose zeros are the parameters of the Bethe wave function for the ground state of the system. As is known, this polynomial satisfies the Baxter T–Q equation. This equation also has a second independent solution corresponding to the same eigenvalue of the transfer matrix T. We use this solution to find the derivative of the ground-state energy of the XXZ chain with respect to the crossing parameter . This derivative is directly related to one of the spin–spin correlators, which appears to be . In turn, this correlator gives the average number of spin strings for the ground state of the chain, . All these simple formulas fail if the number N of chain sites is even.     

Kinetics of curing of epoxy oligomers with adamantane diamines

The kinetics of curing of diglycidyl ester of diphenylolpropane (the first homolog of epoxy-diane oligomers) with diaminomethyladamantane is studied. It is shown that, at the initial stage, the autocatalytic polycondensation is developed which is characterized by an increase in viscosity, branching of a macromolecule, and increasing intermolecular interactions.     

Specificity of the application of disperse and fibrous fillers in heterophase polymer materials

The mechanism of the reinforcing effect of fillers in polymer composition is studied and the relation between the properties and structure of materials is established. It is shown that, upon the addition of even a small amount of filler, properties of polymers change markedly due to intermolecular interactions. Variations in the composition of filled polymers and conditions of their preparation make it possibly to regulate properties of polymers within noticeably wide ranges. Specific features of polymer compositions filled with polymer fibers, the effect of fiber length, and the degree of orientation on the strength of composition are considered. For crosslinked epoxy urethane polymers, the effect of glass and polycaproamide (capron) fibers on the mechanical properties of polymer clutches in glassy and rubbery states is studied. The possibility to realize the shape memory effect for shrinkable filled polymer clutches is demonstrated.     

Three-coloring statistical model with domain wall boundary conditions: Trigonometric limit

We consider a nontrivial trigonometric limit of the three-coloring statistical model with the domain wall boundary conditions. In this limit, we solve the previously constructed functional equations and find a new determinant representation for the partial partition functions.     

Luminescence Technique in the Environmental Control

Luminescence analysis due to its high sensitivity and rather simple equipment is widely used in the environmental control. The most interesting are some methods for the determination of organic pollutants such as oil products, phenols, anionic and cationic surfactants, formaldehyde in waters of different origin, soils, ambient air.     

A Novel Type of Crown Ether‐Containing Metal Ions Optical Sensors Based on Polymer‐Stabilized Cholesteric Liquid Crystalline Films

For the first time, the films based on polymer‐stabilized cholesteric composites containing crown ether fragments with the optical properties sensitive to the complexation with potassium and barium ions were obtained. The complexation with these ions leads to blue spectral shift of the selective light reflection of planar cholesteric texture of composite films. Peculiarities of spectral changes and kinetics of selective light reflection shift were studied. The proposed approach can be used for the creation of the effective and selective sensor materials for different ions or groups of ions.