Quantum phase transitions and thermodynamic properties in highly anisotropic magnets

The systems exhibiting quantum phase transitions (QPT) are investigated within the Ising model in the transverse field and Heisenberg model with easy-plane single-site anisotropy. Near QPT a correspondence between parameters of these models and of quantum phi^4 model is established. A scaling analysis is performed for the ground-state properties. The influence of the external longitudinal magnetic field on the ground-state properties is investigated, and the corresponding magnetic susceptibility is calculated. Finite-temperature properties are considered with the use of the scaling analysis for the effective classical model proposed by Sachdev. Analytical results for the ordering temperature and temperature dependences of the magnetization and energy gap are obtained in the case of a small ground-state moment. The forms of dependences of observable quantities on the bare splitting (or magnetic field) and renormalized splitting turn out to be different. A comparison with numerical calculations and experimental data on systems demonstrating magnetic and structural transitions (e.g., into singlet state) is performed.Comment: 46 pages, RevTeX, 6 figure

Energetically optimal dimensions of parallelepiped-shaped industrial structures

Technical structures with a parallelepiped form are frequently used in various areas of industry. For example, as fluid containers, ice and minerals piles, underground and surface storages and cooling chambers. A task of determining the optimum dimensions of the structure to minimize the energy expenses to support a normative temperature in the structure arises. The minimum surface area of the structure at a given volume is accepted as a criterion of optimality. A problem of unconstrained optimization for a structure with a parallelepiped form was formulated and solved. Equations to determine the optimum dimensions of width, height and length of the structure were obtained. It was determined that a cube is the most optimal form

Influence of air temperature on thaw depth of a road foundation

The expected thaw depth of the foundation soil is one of the parameters influencing the selection of technical solutions of road design in the permafrost area. The purpose of this research is a quantitative assessment of the degree of influence of air temperature on thaw depth of the road foundation soil in the permafrost area. A standard formula to calculate thaw depth of melting bodies of flat symmetry obtained through a solution of the one phase Stefan problem at boundary conditions of the first kind was used for the analysis. An algorithm using an analytical formula to assess the influence of the main initial parameters and accuracy of their determination on the resulting value, the thaw depth of the soil, is proposed. The results of the calculations are presented in a graphical form displaying the influence of average air temperature and the accuracy of its setting on the thaw depth of the road foundation soil. It was determined that the degree of change in thaw depth is non-linear and depends on both the average air temperature and on the accuracy with which it is set. For every average air temperature value there is a specific measure of required accuracy for thermal calculations so that the error of thaw depth determination does not exceed the permitted error. A 3D chart showing the expected percentage error in thaw depth forecasting depending on the average air temperature and the accuracy of its setting for an array of initial values was created

Effect of pressure on the magnetic phase diagram of the antiferromagnetic spin-density-wave alloy Cr-1.6% Si

A neutron diffraction experiment has been performed to study the effects of high pressure on the magnetic phase diagram of a single crystal specimen of Cr-1.6%Si. At applied pressures up to 0.49 GPa there are two clear transitions. At T{sub NC} there is a transition from a paramagnetic (P) to a commensurate spin density wave (CSDW), while at lower temperatures there is a transition to a mixed state where the CSDW seems to coexist with an incommensurate SDW (ISDW) state. T{sub NC} decreases with the application of pressure while the transition temperature T{sub CI} to the mixed C-I state seems to be insensitive to pressure. At 0.69 GPa the ISDW state disappears while the P-C transition changes drastically