Free Energy of the Eight Vertex Model with an Odd Number of Lattice Sites

We calculate the bulk contribution for the doubly degenerated largest eigenvalue of the transfer matrix of the eight vertex model with an odd number of lattice sites N in the disordered regime using the generic equation for roots proposed by Fabricius and McCoy. We show as expected that in the thermodynamic limit the result coincides with the one in the N even case.Comment: 11 pages LaTeX New introduction, Method change

The development of blockchain technology in Russia : outlook and trends

Purpose: The article addresses the issue of new scientific decisions shaping with respect to the study of problems, current trends and perspectives of blockchain technology usage in the Russian Federation. Design/methodology/approach: To achieve the objectives of this study the increasing interest to blockchain technology in Russia was discussed. Findings: The article determined main problems in blockchain technology which includes gaps in legislative regulation; the existence of a considerable number of projects that are undergoing the development stage and that have not proved own economic feasibility yet; incomplete understanding of the blockchain spheres’ implementation by state officials, society and business representatives as well as expected outcomes according to the amount and time of their receiving; disputes on cryptocurrencies turnover in the country’s territory and their influence in the national economy. Practical implications: The study has demonstrated the interest growth mainly by businesses to the usage of blockchain technology in order to improve own competitiveness and to obtain additional benefits, including the form of their profits. Originality/value: The research has also determined the area of further key studies in blockchain technology usage in Russia and the world.peer-reviewe

Ground State of the Quantum Symmetric Finite Size XXZ Spin Chain with Anisotropy Parameter Δ=1/2\Delta = {1/2}

We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for $U_q(sl(2))$ symmetry of the Hamiltonian. More precisely, we find one nontrivial solution, corresponding to the ground state of the system with anisotropy parameter $\Delta = {1/2}$ corresponding to $q^3 = -1$.Comment: 6 page

Asymptotics of Toeplitz Determinants and the Emptiness Formation Probability for the XY Spin Chain

We study an asymptotic behavior of a special correlator known as the Emptiness Formation Probability (EFP) for the one-dimensional anisotropic XY spin-1/2 chain in a transverse magnetic field. This correlator is essentially the probability of formation of a ferromagnetic string of length $n$ in the antiferromagnetic ground state of the chain and plays an important role in the theory of integrable models. For the XY Spin Chain, the correlator can be expressed as the determinant of a Toeplitz matrix and its asymptotical behaviors for $n \to \infty$ throughout the phase diagram are obtained using known theorems and conjectures on Toeplitz determinants. We find that the decay is exponential everywhere in the phase diagram of the XY model except on the critical lines, i.e. where the spectrum is gapless. In these cases, a power-law prefactor with a universal exponent arises in addition to an exponential or Gaussian decay. The latter Gaussian behavior holds on the critical line corresponding to the isotropic XY model, while at the critical value of the magnetic field the EFP decays exponentially. At small anisotropy one has a crossover from the Gaussian to the exponential behavior. We study this crossover using the bosonization approach.Comment: 40 pages, 9 figures, 1 table. The poor quality of some figures is due to arxiv space limitations. If You would like to see the pdf with good quality figures, please contact Fabio Franchini at "[email protected]

Exact expressions for correlations in the ground state of the dense O(1) loop model

Conjectures for analytical expressions for correlations in the dense O$(1)$ loop model on semi infinite square lattices are given. We have obtained these results for four types of boundary conditions. Periodic and reflecting boundary conditions have been considered before. We give many new conjectures for these two cases and review some of the existing results. We also consider boundaries on which loops can end. We call such boundaries ''open''. We have obtained expressions for correlations when both boundaries are open, and one is open and the other one is reflecting. Also, we formulate a conjecture relating the ground state of the model with open boundaries to Fully Packed Loop models on a finite square grid. We also review earlier obtained results about this relation for the three other types of boundary conditions. Finally, we construct a mapping between the ground state of the dense O$(1)$ loop model and the XXZ spin chain for the different types of boundary conditions.Comment: 25 pages, version accepted by JSTA

Hybrid Organic–Inorganic Halide Post-Perovskite 3-Cyanopyridinium Lead Tribromide for Optoelectronic Applications

2D halide perovskite-like semiconductors are attractive materials for various optoelectronic applications, from photovoltaics to lasing. To date, the most studied families of such low-dimensional halide perovskite-like compounds are Ruddlesden–Popper, Dion–Jacobson, and other phases that can be derived from 3D halide perovskites by slicing along different crystallographic directions, which leads to the spatially isotropic corner-sharing connectivity type of metal-halide octahedra in the 2D layer plane. In this work, a new family of hybrid organic–inorganic 2D lead halides is introduced, by reporting the first example of the hybrid organic–inorganic post-perovskite 3-cyanopyridinium lead tribromide (3cp)PbBr3. The post-perovskite structure has unique octahedra connectivity type in the layer plane: a typical “perovskite-like” corner-sharing connectivity pattern in one direction, and the rare edge-sharing connectivity pattern in the other. Such connectivity leads to significant anisotropy in the material properties within the inorganic layer plane. Moreover, the dense organic cation packing results in the formation of 1D fully organic bands in the electronic structure, offering the prospects of the involvement of the organic subsystem into material's optoelectronic properties. The (3cp)PbBr3 clearly shows the 2D quantum size effect with a bandgap around 3.2 eV and typical broadband self-trapped excitonic photoluminescence at temperatures below 200 K

Thermal entanglement in three-qubit Heisenberg models

We study pairwise thermal entanglement in three-qubit Heisenberg models and obtain analytic expressions for the concurrence. We find that thermal entanglement is absent from both the antiferromagnetic $XXZ$ model, and the ferromagnetic $XXZ$ model with anisotropy parameter $\Delta\ge 1$. Conditions for the existence of thermal entanglement are discussed in detail, as is the role of degeneracy and the effects of magnetic fields on thermal entanglement and the quantum phase transition. Specifically, we find that the magnetic field can induce entanglement in the antiferromagnetic $XXX$ model, but cannot induce entanglement in the ferromagnetic $XXX$ model.Comment: 9 pages, 6 figures, minor revisions, resubmitted to J. Phys.

Методика выявления перспективных зон для развития велошеринга в городском пространстве

Purpose: to present the author's methodology for locating perspective zones for bicycle sharing infrastructure development tested on the example of certain districts of the city of Moscow.Methods: the study is based on the application content-analysis of scientific publications and legal documents on bicycle sharing, analysis of statistical data and desk research of spatial location of urban point of attraction. The authors used visual observation and the method comparative analysis to choose the optimal zone for bicycle sharing development to test the proposed method.Results: the analysis of scientific research on the effective location points of bicycle sharing infrastructure is carried out. The research showed the need for the development of a methodology for locating perspective zones for bicycle sharing development in Moscow city. A method has been developed to identify the territories of the city that are most promising for the development of cycling infrastructure. The article offers the system of assessment of the level of development of infrastructure, which allows to perform a comparative analysis of the identified zones to make a conclusion on the prospect of development of the cycling infrastructure.Conclusions and Relevance: the proposed methodology for locating perspective zones for bicycle sharing infrastructure includes several stages: 1) identification of geographical points of attraction for bicycle-users, 2) selection of the most prospective areas containing maximum amount of point of attraction, 3) assessment of the cycling infrastructure development based on the simplified assessment system. It allows to locate perspective zones for cycling and for balancing the location organizing of the sharing infrastructure for cycling development in urban space.Целью статьи является представление авторской методики выявления перспективных зон для развития шеринговой велоинфраструктуры, апробированной на примере отдельных районов города Москвы.Методы. Исследование основано на контент-анализе научных публикаций отечественных и зарубежных ученых и практиков, нормативно-правовой базы в области развития велошеринга, анализе статистических данных, кабинетных исследованиях пространственного размещения городских объектов, являющихся точками притяжения жителей города. Для тестирования предложенной авторами методики использовался метод визуального наблюдения уровня развития велоинфраструктуры, методы сравнительного анализа для выявления перспективных зон развития велошеринга.Результаты работы. Выполнен анализ научных исследований по вопросам эффективного размещения велошеринговой инфраструктуры. Показана необходимость разработки методики выявления перспективных зон для развития велошеринговой инфраструктуры в городе Москве. Разработана методика выявления территорий города, наиболее перспективных для развития велоинфраструктуры. Предложена система оценки уровня развития инфраструктуры, позволяющая выполнить сравнительный анализ выявленных зон для получения заключения о перспективности развития в них велотранспортной инфраструктуры.Выводы. Предложенная в статье методика выявления перспективных зон для развития велошеринговой инфраструктуры состоит из ряда этапов, в результате выполнения которых: 1) выявляются географические объекты, относящиеся к точкам притяжения пользователей велотранспортной инфраструктуры, 2) определяются наиболее перспективные территории по числу точек притяжения, 3) оценивается уровень развития велотранспортной инфраструктуры на данных территориях на основе упрощенной системы оценок. Это позволяет определить перспективные зоны организации движения велосипедистов и сбалансировать территориальное размещение объектов для развития велотранспорта в городском пространстве

Lattice fermion models with supersymmetry

We investigate a family of lattice models with manifest N=2 supersymmetry. The models describe fermions on a 1D lattice, subject to the constraint that no more than k consecutive lattice sites may be occupied. We discuss the special properties arising from the supersymmetry, and present Bethe ansatz solutions of the simplest models. We display the connections of the k=1 model with the spin-1/2 antiferromagnetic XXZ chain at \Delta=-1/2, and the k=2 model with both the su(2|1)-symmetric tJ model in the ferromagnetic regime and the integrable spin-1 XXZ chain at \Delta=-1/\sqrt{2}. We argue that these models include critical points described by the superconformal minimal models.Comment: 28 pages. v2: added new result on mapping to XXZ chai