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

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

Connected components of spaces of Morse functions with fixed critical points

Let $M$ be a smooth closed orientable surface and $F=F_{p,q,r}$ be the space of Morse functions on $M$ having exactly $p$ critical points of local minima, $q\ge1$ saddle critical points, and $r$ critical points of local maxima, moreover all the points are fixed. Let $F_f$ be the connected component of a function $f\in F$ in $F$. By means of the winding number introduced by Reinhart (1960), a surjection $\pi_0(F)\to{\mathbb Z}^{p+r-1}$ is constructed. In particular, $|\pi_0(F)|=\infty$, and the Dehn twist about the boundary of any disk containing exactly two critical points, exactly one of which is a saddle point, does not preserve $F_f$. Let $\mathscr D$ be the group of orientation preserving diffeomorphisms of $M$ leaving fixed the critical points, ${\mathscr D}^0$ be the connected component of ${\rm id}_M$ in $\mathscr D$, and ${\mathscr D}_f\subset{\mathscr D}$ the set of diffeomorphisms preserving $F_f$. Let ${\mathscr H}_f$ be the subgroup of ${\mathscr D}_f$ generated by ${\mathscr D}^0$ and all diffeomorphisms $h\in{\mathscr D}$ which preserve some functions $f_1\in F_f$, and let ${\mathscr H}_f^{\rm abs}$ be its subgroup generated ${\mathscr D}^0$ and the Dehn twists about the components of level curves of functions $f_1\in F_f$. We prove that ${\mathscr H}_f^{\rm abs}\subsetneq{\mathscr D}_f$ if $q\ge2$, and construct an epimorphism ${\mathscr D}_f/{\mathscr H}_f^{\rm abs}\to{\mathbb Z}_2^{q-1}$, by means of the winding number. A finite polyhedral complex $K=K_{p,q,r}$ associated to the space $F$ is defined. An epimorphism $\mu:\pi_1(K)\to{\mathscr D}_f/{\mathscr H}_f$ and finite generating sets for the groups ${\mathscr D}_f/{\mathscr D}^0$ and ${\mathscr D}_f/{\mathscr H}_f$ in terms of the 2-skeleton of the complex $K$ are constructed.Comment: 12 pages with 2 figures, in Russian, to be published in Vestnik Moskov. Univ., a typo in theorem 1 is correcte

Quantum Heisenberg antiferromagnet on low-dimensional frustrated lattices

Using a lattice-gas description of the low-energy degrees of freedom of the quantum Heisenberg antiferromagnet on the frustrated two-leg ladder and bilayer lattices we examine the magnetization process at low temperatures for these spin models. In both cases the emergent discrete degrees of freedom implicate a close relation of the frustrated quantum Heisenberg antiferromagnet to the classical lattice gas with finite nearest-neighbor repulsion or, equivalently, to the Ising antiferromagnet in a uniform magnetic field. Using this relation we obtain analytical results for thermodynamically large systems in the one-dimensional case. In the two-dimensional case we perform classical Monte Carlo simulations for systems of up to $100 \times 100$ sites.Comment: Submitted to Teoreticheskaya i Matematicheskaya Fizika (special issue dedicated to the 90th anniversary of Professor Sergei Vladimirovich Tyablikov

Geometry of integrable dynamical systems on 2-dimensional surfaces

This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous invariants involved in this classification are the left equivalence classes of period or monodromy functions, and the cohomology classes of period cocycles, which can be expressed in terms of Puiseux series. We also study the problem of Hamiltonianization of these integrable vector fields by a compatible symplectic or Poisson structure.Comment: 31 pages, 12 figures, submitted to a special issue of Acta Mathematica Vietnamic

Topology of the spaces of Morse functions on surfaces

Let $M$ be a smooth closed orientable surface, and let $F$ be the space of Morse functions on $M$ such that at least $\chi(M)+1$ critical points of each function of $F$ are labeled by different labels (enumerated). Endow the space $F$ with $C^\infty$-topology. We prove the homotopy equivalence $F\sim R\times{\widetilde{\cal M}}$ where $R$ is one of the manifolds ${\mathbb R}P^3$, $S^1\times S^1$ and the point in dependence on the sign of $\chi(M)$, and ${\widetilde{\cal M}}$ is the universal moduli space of framed Morse functions, which is a smooth stratified manifold. Morse inequalities for the Betti numbers of the space $F$ are obtained.Comment: 15 pages, in Russia

Child Internalizing Problems in Ukraine: The Role of Prosocial and Antisocial Friends and Generalized Self-Efficacy

Child internalizing problems in Ukraine: the role of prosocial and antisocial friends and generalized self-efficacy / Viktor Burlaka, Oleksii Serdiuk, Valerii Sokurenko and etc. // Societies. – 2022. – Vol. 12, Issue 5. – Art. 144. – DOI: https://doi.org/10.3390/soc12050144.Burlaka, V.; Serdiuk, O.; Sung Hong, J.; O’Donnell, L.A.; Maksymenko, S.; Panok, V.; Danylenko, H.; Linskiy, I.; Sokurenko, V.; Churakova, I.; Ilchyshyn, N. Child Internalizing Problems in Ukraine: The Role of Prosocial and Antisocial Friends and Generalized Self-Efficacy. Societies 2022, 12, 144. https://doi.org/10.3390/soc12050144.Burlaka V, Serdiuk O, Sung Hong J, O’Donnell LA, Maksymenko S, Panok V, Danylenko H, Linskiy I, Sokurenko V, Churakova I, Ilchyshyn N. Child Internalizing Problems in Ukraine: The Role of Prosocial and Antisocial Friends and Generalized Self-Efficacy. Societies. 2022; 12(5):144. https://doi.org/10.3390/soc12050144Burlaka, Viktor, Oleksii Serdiuk, Jun Sung Hong, Lisa A. O’Donnell, Serhii Maksymenko, Vitalii Panok, Heorhii Danylenko, Igor Linskiy, Valerii Sokurenko, Iuliia Churakova, and Nadiya Ilchyshyn. 2022. "Child Internalizing Problems in Ukraine: The Role of Prosocial and Antisocial Friends and Generalized Self-Efficacy" Societies 12, no. 5: 144. https://doi.org/10.3390/soc12050144.У дослідженні обговорюються культурні та гендерні аспекти соціалізації дитини в контексті асоціальних і просоціальних друзів, а також розвиток проблем інтерналізованої поведінки.The current study examines the association between peer behaviors, self-efficacy, and internalizing symptoms in a sample of 1545 children aged 11 to 13 years old who attended middle schools in eastern Ukraine. We used structural equation modeling (SEM) to examine the role of self-efficacy in the relationship between child internalizing behaviors (anxiety, depression, and somatic complaints) and exposure to prosocial and antisocial friends among girls and boys. Higher self-efficacy was linked with fewer internalizing symptoms for girls and boys. For both boys and girls, exposure to prosocial friends was not statistically associated with changes in internalizing behaviors. However, girls and boys who reported having more antisocial friends had significantly more internalizing symptoms. For girls, association with a greater number of prosocial friends and fewer antisocial friends has been linked with higher self-efficacy and fewer internalizing symptoms. For boys, having more prosocial friends was also linked with higher self-efficacy and fewer internalizing symptoms; however, there was no statistically significant association between having more antisocial friends and self-efficacy. The study discusses the cultural and gender aspects of child socialization in the context of antisocial and prosocial friends, and the development of internalizing behavior problems.В исследовании обсуждаются культурные и гендерные аспекты социализации ребенка в контексте асоциальных и просоциальных друзей, а также развитие проблем интернализирующего поведения