Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices

We consider the repulsive Hubbard model on three highly frustrated one-dimensional lattices -- sawtooth chain and two kagom\'{e} chains -- with completely dispersionless (flat) lowest single-electron bands. We construct the complete manifold of {\em exact many-electron} ground states at low electron fillings and calculate the degeneracy of these states. As a result, we obtain closed-form expressions for low-temperature thermodynamic quantities around a particular value of the chemical potential $\mu_0$. We discuss specific features of thermodynamic quantities of these ground-state ensembles such as residual entropy, an extra low-temperature peak in the specific heat, and the existence of ferromagnetism and paramagnetism. We confirm our analytical results by comparison with exact diagonalization data for finite systems.Comment: 20 pages, 12 figures, 2 table

Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem

We investigate the location and nature of the para-ferro transition of interacting electrons in dispersionless bands using the example of the Hubbard model on the Tasaki lattice. This case can be analyzed as a geometric site-percolation problem where different configurations appear with nontrivial weights. We provide a complete exact solution for the 1D case and develop a numerical algorithm for the 2D case. In two dimensions the paramagnetic phase persists beyond the uncorrelated percolation point, and the grand-canonical transition is via a first-order jump to an unsaturated ferromagnetic phase.Comment: 6 pages, 5 figure

Bile production features in case of ischemic-reperfusion syndrome of limbs, abdominal trauma complicated with massive blood loss

The level of total bile acids in bile decreased in the groups of experimental animals in comparison with the control group. In the group of animals with simulated ischemic-reperfusion injury level of total bile acids in bile reached the minimal values in on the 3rd day, increasing was showed after on the 7th day, however level still remained lower than in control group. In EG-2 and EG-3 there was a unidirectional decreasing of the index by the seventh day, but in EG-3 these changes were more significant. Consequently, the level of cholesterol in the bile due to simulated injuries decreased in EG-1 and reached the minimal values in on the 3rd day and slightly increased to the seventh day of observation. In EG-2 the index gradually increased to the seventh day of observation. In EG-3 the maximum increasing was observed until the third day, after which it was at the same level. The analysis of the obtained indices testifies to the negative influence of ischemic-reperfusion syndrome on the level of cholesterol in the bile. Described changes influenced the cholato-cholesterol ratio, which was decreasing in all experimental groups. The most significant changes were in EG-3 in which abdominal trauma and hypovolemic shock were combined with ischemic-reperfusion limb syndrome. In the conditions of an experimental trauma with an ischemic-reperfusion injury of the lower limbs, there is a violation of the indices of the biliary function of the liver, which manifest themselves as a significant reduction of the level of total bile acids in the bile with increasing cholesterol concentration

ESR modes in a Strong-Leg Ladder in the Tomonaga-Luttinger Liquid Phase

Magnetic excitations in the strong-leg quantum spin ladder compound (C$_7$H$_{10}$N)$_2$CuBr$_4$ (known as DIMPY) in the field-induced Tomonaga-Luttinger spin liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual non-linear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe its ESR observability to the uniform Dzyaloshinskii-Moriya interaction

ПОНЯТТЯ ЕФЕКТИВНОСТІ РЕГІОНАЛЬНОЇ ПРОМИСЛОВОЇ ПОЛІТИКИ

At the theoretical and practical levels it has been proved that the mechanism of regional industrial policy should be adapted to the social and economic state of the region's development, taking into account the features of the economic structure and the state of provision of economic resources. There is a problem of searching for a variant of the most effective mechanism of regional industrial policy. Since there are no specific performance criteria for today, it is advisable to study in depth the concept of "the effectiveness of regional industrial policy."The aim of the article is to study the theoretical and practical aspects of the concept of "the effectiveness of regional industrial policy." The main part of the research is aimed at delineating the semantic load of the concepts "economic effect", "economic efficiency" and "productivity (productivity)."The essential characteristics of the concept of "the effectiveness of regional industrial policy" have been substantiated in the article. A model for assessing the efficiency and effectiveness of economic policy has been proposed.На теоретическом и практическом уровнях доказано, что механизм региональной промышленной политики должен быть адаптирован к социально-экономического состояния развития региона, учитывать особенности экономической структуры и состояние обеспечения экономическими ресурсами. Возникает проблема поиска варианта наиболее эффективного механизма региональной промышленной политики. Поскольку на сегодняшний день неопределенно четких критериев эффективности, целесообразно углубленное исследование понятия «эффективность региональной промышленной политики».Целью статьи является исследование теоретических и практических аспектов понятия «эффективность региональной промышленной политики». Основная часть исследования направлена на разграничение смысловой нагрузки понятий «экономический эффект», «экономическая эффективность» и «результативность (производительность)». В статье обоснована сущностные характеристики понятия «эффективность региональной промышленной политики». Предложена модель оценки эффективности и результативности экономической политики. На теоретичному та практичному рівнях доведено, що механізм регіональної промислової політики повинен бути адаптованим до соціально-економічного стану розвитку регіону, враховувати особливості його економічної структури та стан забезпечення економічними ресурсами. Постає проблема пошуку варіанту найбільш ефективного механізму регіональної промислової політики. Оскільки на сьогоднішній день невизначено чітких критеріїв ефективності, доцільним є поглиблене дослідження поняття «ефективність регіональної промислової політики».Метою статті є дослідження теоретичних та практичних аспектів поняття «ефективність регіональної промислової політики». Основна частина дослідження спрямована на розмежування змістового навантаження понять «економічний ефект», «економічна ефективність» та «результативність (продуктивність)». У статті обґрунтовано сутнісні характеристики поняття «ефективність регіональної промислової політики». Запропоновано модель оцінки ефективності та результативності економічної політики

Homotopy types of stabilizers and orbits of Morse functions on surfaces

Let $M$ be a smooth compact surface, orientable or not, with boundary or without it, $P$ either the real line $R^1$ or the circle $S^1$, and $Diff(M)$ the group of diffeomorphisms of $M$ acting on $C^{\infty}(M,P)$ by the rule $h\cdot f\mapsto f \circ h^{-1}$, where $h\in Diff(M)$ and $f \in C^{\infty}(M,P)$. Let $f:M \to P$ be a Morse function and $O(f)$ be the orbit of $f$ under this action. We prove that $\pi_k O(f)=\pi_k M$ for $k\geq 3$, and $\pi_2 O(f)=0$ except for few cases. In particular, $O(f)$ is aspherical, provided so is $M$. Moreover, $\pi_1 O(f)$ is an extension of a finitely generated free abelian group with a (finite) subgroup of the group of automorphisms of the Reeb graph of $f$. We also give a complete proof of the fact that the orbit $O(f)$ is tame Frechet submanifold of $C^{\infty}(M,P)$ of finite codimension, and that the projection $Diff(M) \to O(f)$ is a principal locally trivial $S(f)$-fibration.Comment: 49 pages, 8 figures. This version includes the proof of the fact that the orbits of a finite codimension of tame action of tame Lie group on tame Frechet manifold is a tame Frechet manifold itsel