Unconventional phase transitions in strongly anisotropic 2D (pseudo)spin systems

We have applied a generalized mean-field approach and quantum Monte-Carlo technique for the model 2D S = 1 (pseudo)spin system to find the ground state phase with its evolution under application of the (pseudo)magnetic field. The comparison of the two methods allows us to clearly demonstrate the role of quantum effects. Special attention is given to the role played by an effective single-ion anisotropy (»on-site correlation»). © 2018 The Authors, published by EDP Sciences.The research was supported by the Government of the Russian Federation, Program 02.A03.21.0006 and by the Ministry of Education and Science of the Russian Federation, projects Nos. 2277 and 5719

General model selection estimation of a periodic regression with a Gaussian noise

This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of arbitrary projective estimates, which does not need the knowledge of the noise correlation function, is proposed. A non-asymptotic upper bound for quadratic risk (oracle inequality) has been derived under mild conditions on the noise. For the Ornstein-Uhlenbeck noise the risk upper bound is shown to be uniform in the nuisance parameter. In the case of gaussian white noise the constructed procedure has some advantages as compared with the procedure based on the least squares estimates (LSE). The asymptotic minimaxity of the estimates has been proved. The proposed model selection scheme is extended also to the estimation problem based on the discrete data applicably to the situation when high frequency sampling can not be provided

The influence of local correlations on the phase states in the model of semi-hard-core bosons on a square lattice

The work considers a model of charged "semi-hard-core" bosons on a square lattice with a possible filling number at each node, ranging from 0 to 2. Temperature phase diagrams of the model are obtained using numerical Monte Carlo quantum simulation methods, and the influence of local charge correlations is examined. Comparison with results from mean-field methods shows that local charge correlations contribute to an increased role of quantum fluctuations in the formation of phase states.Comment: 5 pages, 2 figure

Phase Diagram of Semi-Hard-Core Bosons on a Square Lattice

Abstract: Phase diagrams of charged “semi-hard-core” bosons are studied in the mean field approximation. An increase in the parameter of local correlations is shown to lead to the transformation of the phase diagram of the system from the form characteristic of “hard-core” bosons to the limiting form with a parabolic dependence of the critical temperature of charge ordering on the boson concentration. The evolution between these limiting cases is dependent on the ratio between the model parameters and is accompanied by various effects, such as the change in the phase transition type, the appearance of new order–order transition, and the appearance of new critical points. © 2021, Pleiades Publishing, Ltd.Ministry of Education and Science of the Russian Federation, Minobrnauka: FEUZ-2020-0054; Government Council on Grants, Russian FederationThis work was supported by the program 211 of the Government of the Russian Federation (Agreements no. 02.A03.21.0006) and the Ministry of Education and Science of the Russian Federation (project no. FEUZ-2020-0054

Magnetic properties and structure of TiO2-Mn (0.73 %) nanopowders: The effects of electron irradiation and vacuum annealing

Nanopowder TiO2-0.73 % Mn was synthesized by the sol-gel method. Thermal treatment of the samples was carried out in vacuum at a temperature of 500°C. Magnetic properties were studied in the temperature range from 2 to 850 K. The effects of electron irradiation and vacuum annealing on the EPR spectra and magnetic properties of TiO2-Mn powder are discussed. It was established that a part of manganese ions in the anatase crystal lattice interacts antiferromagnetically, which causes a decrease in magnetization as compared to the result of the calculation for non-interacting ions. Vacuum annealing leads to the formation of oxygen vacancies and, at the same time, to a noticeable increase in the ferromagnetic contribution to magnetization, especially, after preliminary electron irradiation. We assume that the ferromagnetic contribution to the magnetization appears either due to incomplete compensation of antiferromagnetically directed moments of manganese ions, or due to positive exchange interactions of Mn ions via defects in the TiO2 lattice. It is shown that the temperature of magnetic disordering in samples with a spontaneous magnetic moment exceeds 600°C. © 2019, Institute for Metals Superplasticity Problems of Russian Academy of Sciences. All rights reserved

Efficient Certified Resolution Proof Checking

We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms a state-of-the-art checker by two orders of magnitude. We then formalize the theory underlying propositional proof checking in Coq, and extract a correct-by-construction proof checker for our format from the formalization. An empirical evaluation using 280 unsatisfiable instances from the 2015 and 2016 SAT competitions shows that this certified checker usually performs comparably to a state-of-the-art non-certified proof checker. Using this format, we formally verify the recent 200 TB proof of the Boolean Pythagorean Triples conjecture

Unconventional magnetism of non-uniform distribution of Co in TiO2 nanoparticles

High-resolution transmission electron microscopy (HRTEM), X-ray diffraction (XRD) analysis, electron paramagnetic resonance (EPR), X-ray absorption spectroscopy (XAS), magnetic methods, and density-functional theory (DFT) calculations were applied for the investigations of Co-doped anatase TiO2 nanoparticles (∼20 nm). It was found that high-spin Co2+ ions prefer to occupy the interstitial positions in the TiO2 lattice which are the most energetically favourable in compare to the substitutional those. A quantum mechanical model which operates mainly on two types of Co2+ – Co2+ dimers with different negative exchange interactions and the non-interacting paramagnetic Co2+ ions provides a satisfactorily description of magnetic properties for the TiO2:Co system. © 2020 Elsevier B.V.Russian Foundation for Basic Research. Ministry of Science and Higher Education of the Russian Federatio

Features of the Domain Boundaries of a Highly Anisotropic (S = 1) Antiferromagnet near the Transition to the Quantum Paramagnet Phase

Abstract: It is shown that the structure of antiphase domain boundaries in the antiferromagnetic (AFM) phase of a highly anisotropic magnet with S = 1 on a two-dimensional square lattice depends greatly on single-ion anisotropy parameter D. Computer modeling on large square lattices illustrates the changes in the boundary structure from the quantum paramagnet (QP) to the XY phase, including the intermediate QP–XY phase at fairly small variations in positive D. © 2019, Allerton Press, Inc.2277, 5719; Government Council on Grants, Russian FederationThis work was supported by Program 211 of the Government of the Russian Federation, project no. 02.A03.21.0006; and by the RF Ministry of Science and Higher Education, project nos. 2277 and 5719

Influence of Local Correlations on the “Homogeneous Insulator–Superconductor” Transition in the Domain Boundaries of the Charge-Order Phase of a 2D System of a Mixed Valence

Abstract—It is demonstrated in the (pseudo)spin S = 1 formalism that the structure of antiphase domain boundaries in the phase of charge ordering of a mixed-valence system of the Cu1+, 2+, 3+ “triplet” type in cuprates on a two-dimensional square lattice depends to a considerable extent on on-site correlation parameter U. The results of computer modeling on large square lattices illustrate the change in the boundary structure (from a homogeneous monovalent nonconducting structure of the Cu2+ type to a filamentary superconducting one) induced by a relatively small variation of positive U values. © 2018, Pleiades Publishing, Ltd.Ministry of Education and Science of the Russian Federation, Minobrnauka; Government Council on Grants, Russian Federation: 2277, 5719ACKNOWLEDGMENTS This study was supported by Program 211 of the Government of the Russian Federation, agreement no. 02.A03.21.0006, and projects 2277 and 5719 of the Ministry of Education and Science of the Russian Federation

NMR study of magnetic nanoparticles Ni@C

The 61Ni, 13C NMR spectra of carbon encapsulated nickel nanoparticles have been obtained. It has been shown that the cores of the particles consist of metallic nickel with face-centered cubic structure, nickel carbide Ni3C and carbon-nickel solid solution. The carbon shell of nanoparticles is a highly defective structure and close to an amorphous glassy-like carbon. © Published under licence by IOP Publishing Ltd.Ural Branch, Russian Academy of Sciences, UB RAS: 18-10-2-37.The study was performed within the state assignments of the Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences: state program «Function» No АААА-А19-119012990095-0; state program «Magnit» No АААА-А18-118020290129-5 and state program «Alloys». The research also was supported by the project of the complex program of Ural Branch of Russian Academy of Sciences № 18-10-2-37