Classical Heisenberg antiferromagnet on a garnet lattice: a Monte Carlo simulation

We have studied a classical antiferromagnet on a garnet lattice by means of Monte Carlo simulations in an attempt to examine the role of geometrical frustration in Gadolinium Gallium Garnet, Gd3Ga5O12 (GGG). Low-temperature specific heat, magnetisation, susceptibility, the autocorrelation function A(t) and the neutron scattering function S(Q) have been calculated for several models including different types of magnetic interactions and with the presence of an external magnetic field applied along the principal symmetry axes. A model, which includes only nearest-neighbour exchange, J1, neither orders down to the lowest temperature nor does it show any tendency towards forming a short-range coplanar spin structure. This model, however, does demonstrate a magnetic field induced ordering below T ~ 0.01 J1. In order to reproduce the experimentally observed properties of GGG, the simulated model must include nearest neighbour exchange interactions and also dipolar forces. The presence of weak next-to-nearest exchange interactions is found to be insignificant. In zero field S(Q) exhibits diffuse magnetic scattering around positions in reciprocal space where antiferromagnetic Bragg peaks appear in an applied magnetic field.Comment: 8 pages, 8 figures, to appear in PRB (JAN 2001

Investigation of the Heating Processes and Temperature Field of the Frequency-controlled Asynchronous Engine Based on Mathematical Models

The study of the temperature field of the engine for non-stationary modes is done. A numerical simulation of a non-stationary thermal process using dynamic EHD, the characteristic of the rate of rise of temperatures is done. An increase in the temperature of individual parts in the idle interval, when the power of heat release is significantly reduced, is established, and the reverse of the heat flow through the air gap is established. It is shown that the EHD method, in contrast to the FEM, is self-sufficient, which determines its practical value. In various parts of the speed control range in the implementation of various laws of regulation. At the same time, the main electrical, magnetic and additional losses associated with the fundamental voltage harmonics (FVH), and mechanical losses, as well as additional electrical and magnetic losses associated with the higher voltage harmonics, change. When using serial asynchronous engines as frequency-controlled. Permissible under the conditions of heating power is significantly reduced by the power of serial engines. Depending on the synchronous speed, the reduction is from 10 % to 20 %. Given the additional overheating due to higher voltage harmonics, as well as the deterioration of the cooling conditions when adjusting the rotational speed "down" from the nominal, it seems very relevant

Evolution of spin correlations in SrDy2O4 in an applied magnetic field

The development of short- and long-range magnetic order induced in a frustrated zig-zag ladder compound SrDy2O4 by an applied field is studied using neutron diffraction techniques. In zero field, SrDy2O4 lacks long-range magnetic order down to temperatures as low as 60 mK, and the observed powder neutron diffraction (PND) patterns are dominated by very broad diffuse scattering peaks. Single crystal neutron diffraction reveals that the zero-field magnetic structure consists of a collection of antiferromagnetic chains running along the c axis and that there is very little correlation between the chains in the ab plane. In an applied magnetic field, the broad diffuse scattering features in PND are gradually replaced by much sharper peaks, however, the pattern remains rather complex, reflecting the highly anisotropic nature of SrDy2O4. Single crystal neutron diffraction shows that a moderate field applied along the b axis induces an up-up-down magnetic order associated with a 1/3-magnetisation plateau, in which magnetic correlation length in the ab plane is significantly increased, but it nevertheless remains finite. The resolution limited k = 0 peaks associated with a ferromagnetic arrangement appear in powder and single crystal neutron diffraction patterns in fields of 2.5 T and above.Comment: 10 pages, 11 figure

Inframarginal analysis of institute of firm

The paper considers using the microeconomic approach to a study of the influence of specialization and transaction costs on the division of labor that is refereed to in the foreign literature as inframarginal analysis. The subject of the research is a structure of the relations properties rights named a firm. The theme of the research is structures of the economic relations where economic agents can maximize their utility. The structures in turn determine the ways of distribution of the residual rights which determine the structure of the firm. The paper is based on widely known publications by European scientists about the theory of the firm, and the results of works of Australian and Chinese economists which have been given insufficient coverage in the domestic economic science. On the basis of the works of domestic and foreign authors, consistency of the conceptual framework of inframarginal analysis and the terminology of the domestic economic theory, mathematical programming and the theory of decision making is outlined. The author constructed three-dimensional visualization of the functions of maximum utility of economic agents for types of organizational structures which can be formed by economic agents for the achievement of the maximum utility. For the first time a graphic representation of the general inframarginal equilibrium allowing one to determine an optimum configuration for specific conditions of production is offered. The concept of the inframarginal steady firm is introduced. Parallels between methods of operations research and inframarginal analysis are drawn; similarities and distinctions are specified. The procedure of carrying out inframarginal analysis is structured in the form of a decision tree. The practical importance of the work is that in spite of the fact that the models offered in the research don’t yield absolute quantitative results; the obtained conclusions can be used for complex assessment of the condition of the firm, together with traditional tools, such as analysis of financial and economic activities. The theoretical provisions can be used by universities for the improvement of the existing courses on the economic theory.В статье рассматривается применение микроэкономического подхода к исследованию влияния специализации и транзакционных издержек на разделения труда, получившего в зарубежной литературе название инфрамаржинальный анализ. Объектом исследования выступает такая структура отношений собственности, как фирма. Предметом исследования являются структуры экономических отношений, в которых экономическими агентами возможно достижение максимальной полезности. Полученные структуры, в свою очередь, определяют механизм распределения остаточных прав, определяющих структуру фирмы. В основе исследования лежат как широко известные публикации по теории фирмы европейских ученых, так и слабо представленные в отечественной экономической мысли результаты работ австралийских и китайских экономистов. На основе работ отечественных и зарубежных авторов приведено соответствие понятийного аппарата инфрамаржинального анализа отечественным терминам, принятым в экономической теории, математическом программировании и теории принятия решений. Автором составлена трехмерная визуализация функций максимальной полезности экономических агентов для типов организационных структур, которые могут быть образованы экономическими агентами для достижения максимальной полезности. Впервые предложено графическое изображение общего инфрамаржинального равновесия, позволяющее определить оптимальную конфигурацию для конкретных условий производства. Введено понятие инфрамаржинально устойчивой фирмы. Проведены параллели между методами исследования операций и инфрамаржинальным анализом, указаны сходства и различия. Процедура проведения инфрамаржинального анализа структурирована в виде дерева принятия решений. Практическая значимость работы заключается в том, что, несмотря на то, что предложенные в исследовании модели не дают абсолютных количественных результатов, полученные выводы могут быть использованы для комплексной оценки состояния фирмы совместно с традиционными инструментами, такими как анализ финансово-хозяйственной деятельности. Теоретические положения могут быть использованы университетами для развития существующих программ по экономической теории

Magnetic charge and ordering in kagome spin ice

We present a numerical study of magnetic ordering in spin ice on kagome, a two-dimensional lattice of corner-sharing triangles. The magnet has six ground states and the ordering occurs in two stages, as one might expect for a six-state clock model. In spin ice with short-range interactions up to second neighbors, there is an intermediate critical phase separated from the paramagnetic and ordered phases by Kosterlitz-Thouless transitions. In dipolar spin ice, the intermediate phase has long-range order of staggered magnetic charges. The high and low-temperature phase transitions are of the Ising and 3-state Potts universality classes, respectively. Freeze-out of defects in the charge order produces a very large spin correlation length in the intermediate phase. As a result of that, the lower-temperature transition appears to be of the Kosterlitz-Thouless type.Comment: 20 pages, 12 figures, accepted version with minor change

Numerical calculation of the combinatorial entropy of partially ordered ice

Using a one-parameter case as an example, we demonstrate that multicanonical simulations allow for accurate estimates of the residual combinatorial entropy of partially ordered ice. For the considered case corrections to an (approximate) analytical formula are found to be small, never exceeding 0.5%. The method allows one as well to calculate combinatorial entropies for many other systems.Comment: Extended version: 7 pages, 10 figures (v1 is letter-type version

Energy benchmarks for water clusters and ice structures from an embedded many-body expansion

We show how an embedded many-body expansion (EMBE) can be used to calculate accurate \emph{ab initio} energies of water clusters and ice structures using wavefunction-based methods. We use the EMBE described recently by Bygrave \emph{et al.} (J. Chem. Phys. \textbf{137}, 164102 (2012)), in which the terms in the expansion are obtained from calculations on monomers, dimers, etc. acted on by an approximate representation of the embedding field due to all other molecules in the system, this field being a sum of Coulomb and exchange-repulsion fields. Our strategy is to separate the total energy of the system into Hartree-Fock and correlation parts, using the EMBE only for the correlation energy, with the Hartree-Fock energy calculated using standard molecular quantum chemistry for clusters and plane-wave methods for crystals. Our tests on a range of different water clusters up to the 16-mer show that for the second-order M\o{}ller-Plesset (MP2) method the EMBE truncated at 2-body level reproduces to better than 0.1 m$E_{\rm h}$/monomer the correlation energy from standard methods. The use of EMBE for computing coupled-cluster energies of clusters is also discussed. For the ice structures Ih, II and VIII, we find that MP2 energies near the complete basis-set limit reproduce very well the experimental values of the absolute and relative binding energies, but that the use of coupled-cluster methods for many-body correlation (non-additive dispersion) is essential for a full description. Possible future applications of the EMBE approach are suggested