Semiclassical Approximation for the Curie

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Semiclassical Approximation for the Curie – Weiss Model

Journal of Physics: Conference Series. 2021. Vol. 1740. Article 012069.

Булеков А. А.

The paper is devoted to the construction of spectral series and the estimation of the approximation accuracy for the operator of the Curie – Weiss model. In the course of work, the operator is reduced to a tridiagonal form in the subspace of the original space, then to a secondorder difference equation. The admissibility of reducing an operator to a subspace is presented. It is shown that the difference equation can be considered in the discrete semiclassical approximation. In the obtained classical system, the dependence of the turning points on the model parameters is investigated. The asymptotics of the spectrum of the Curie-Weiss operator is calculated and the accuracy of the approximation is estimated.

Research target: Physics Mathematics

Priority areas: mathematics

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Блудов М. В., Journal of Fixed Point Theory and Applications 2026 No. 28 Article 73

In this paper, we study a construction of homotopy invariants of open or closed covers, where the homotopy class is defined relative to a pair (V, r), with V a finite set of points in and r a point in the interior of their convex hull. We show that the simplicial complex of non-balanced subsets associated with (V, r) has the homotopy ...

Added: August 25, 2026

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L.I. Kuzmina, Osipov , Y. V., Kolokoltseva, T. N., Advances in Water Resources 2026 Vol. 213 Article 105335

We study 1D transport of mobilized particles, detached from the solid matrix, in porous media (so-called fines migration). Three types of colloidal-suspension flow models are considered: (i) averaged model for multicomponent colloids with distributed properties; (ii) flow of binary colloids with interacting particles; (iii) discrete system for multicomponent low-concentration colloid. These models account for distributed ...

Added: August 25, 2026

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Modeling the transport and sedimentation of small particles of suspensions and colloids in porous rocks is an important problem in subsurface hydromechanics. Particles entrained in fluid are transported and retained in the rock pores. The filtration process is determined by the number and size of pores and is characterized by porosity—the ratio of the void ...

Added: August 25, 2026

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L.I.Kuzmina, Osipov Y. V., Mathematical notes, ISSN 0001-4346 2025 Vol. 116 No. 6 P. 1251–1261

We consider the displacement of oil by water with active chemical reagents in porous media. A one-dimensional model of reagent transport and deposition is deﬁned by a hyperbolic system of ﬁrst-order equations. The purpose of the article is to ﬁnd the conditions for the existence of a continuous solution with discontinuous boundary and initial conditions. ...

Added: August 25, 2026

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Лукьяненко Д. В., Ragimova A., Мухорина А. et al., European Physical Journal: Special Topics 2026 P. 1–24

Electronic health records (EHRs) contain vast volumes of clinical information that encode complex relationships between diseases. Traditional approaches to the analysis of interrelated or co-occurring diseases have focused on pairwise associations between diagnoses, missing the higher-order structures that characterise multimorbid patients. The present paper offers a narrative review of existing statistical, machine-learning, and artificial intelligence ...

Added: August 20, 2026

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Mazur D., Brandyshev P., Doronin S. V. et al., Electrochimica Acta 2026 Vol. 577 Article 149729

The electric double layer (EDL) at a single-crystal metal surface is controlled not only by the electrolyte composition and the electrode potential, but also by the atomic structure of the surface itself. This makes the Ag(hkl)/NaF interface a stringent test for continuum theories of the EDL. In the third part of our series, we examine ...

Added: August 20, 2026

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Chernov A., European Journal of Mathematics 2026 Vol. 12 Article 48

An induced additive action on a projective variety is a regular action of the group G_a^n on X in P^n with an open orbit that can be extended to a regular action on P^n. Such actions are known to correspond to pairs (A, U), where A is a local algebra and U is a generating subspace lying in the maximal ideal. This paper ...

Added: August 19, 2026

Dynamics of Systems, Mechanisms and Machines (Dynamics). International scientific and technical conference

IEEE Advancing Technology for Humanity, 2025.

Dynamics of Systems, Mechanisms and Machines (Dynamics) ...

Added: August 19, 2026

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Gimaev R., Karpenkov A., Shelkovyi F. et al., Journal of Alloys and Compounds 2026 No. 1080 Article 190307

The magnetothermal properties of the quaternary Fe49Rh46.1Pd3.1Ir1.8 alloy are investigated by a combination of first-principles calculations, structural characterization, magnetometry, calorimetry, and direct measurements of the adiabatic temperature change. An exceptional magnetocaloric response is obtained, with ΔTad reaching −11.9 K in a field of 1.85 T under the discontinuous protocol and −8.6 K under the continuous ...

Added: August 18, 2026

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Vlasenko D., Saranskaia I., Zakharov D., European Physical Journal: Special Topics 2026 P. 1–16

Hypergraphs provide a natural framework for representing neurophysiological interactions distributed across sets of sensors. A key methodological question is how hyperedges should be defined from frequency-resolved electroencephalography/magnetoencephalography (EEG/MEG) data. We demonstrate a construction strategy in which hyperedges are obtained from canonical coherence (caCOH), an extension of coherence that estimates coupling between multidimensional signal spaces. To ...

Added: August 18, 2026

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Borisov D., Katzarkov Ludmil, Sheshmani A. et al., American Journal of Mathematics 2026 Vol. 148 No. 4 P. 1075–1101

It is shown that there are globally defined Lagrangian distributions on the stable loci of derived \mathrm{Quot}-stacks of coherent sheaves on Calabi--Yau four-folds. Dividing by these distributions produces perfectly obstructed smooth stacks with globally defined -1-shifted potentials, whose derived critical loci give back the stable loci of smooth stacks of sheaves in global Darboux form. ...

Added: August 18, 2026

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Богатырев А. Б., Математический сборник 2023 Т. 214 № 3 С. 106–119

Рассматривается клеточное разбиение пространства модулей вещественных кривых рода 2 с отмеченной точкой на единственном вещественном овале. Клетки перечисляются определенными графами, веса которых описывают комплексную структуру на кривой. Показано, что стягивание ребра графа приводит к корневой особенности естественного отображения из весов графа в пространство модулей кривых. ...

Added: August 14, 2026

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Богатырев А. Б., Gendron Q., Успехи математических наук 2023 Т. 78 № 1 С. 209–210

Уравнение Пелля-Абеля — это функциональное уравнение вида P²-DQ² = 1, с заданным многочленом D, свободным от квадратов, и неизвестными многочленами P и Q. Мы показываем, что пространство уравнений Пелля-Абеля с фиксированными степенями D и примитивным решением P является комплексным многообразием. Мы описываем его связные компоненты с помощью эффективно вычислимого инварианта. ...

Added: August 14, 2026

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The best uniform rational approximation of the Sign function on two intervals separated by zero was explicitly found by E. I. Zolotarëv in 1877. The natural extension of this problem to three bands was solved by E. Stiefel in 1961. We indicate the solutions overlooked by the prominent geometer and study their properties. ...

Added: August 14, 2026

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Предложена простая и эффективно реализуемая формула для изменения абелевых интегралов (включая их периоды) при вариации образующих классической группы Шоттки, представляющей риманову поврехность. ...

Added: August 14, 2026

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A Pell–Abel equation is a functional equation of the form P^2-DQ^2=1 , with a given polynomial D free of squares and unknown polynomials P and Q. We show that the space of Pell–Abel equations with the degrees of D and of the primitive solution P fixed is a complex manifold. We describe its connected components ...

Added: August 14, 2026

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Khorunzheva K., Postnikov E., Zakharov D., Chaos, Solitons and Fractals 2026 Vol. 212 No. 2 P. 1–12

Identification of coherent states of spiking neural networks is a fundamental problem of synchronization theory but conventional methods are computationally expensive. We apply the crystallographic ideas of processing periodic structures to the analysis of various states of spiking neuronal networks. In particular, the introduced approach is based on the application of two-dimensional Fourier transform to rasterplots. By the position ...

Added: August 13, 2026

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Beck M. E., Seidov S., Mukhin S., Physical Review A: Atomic, Molecular, and Optical physics 2026

Quantum dissipation is studied in the superradiant phase of the extended Dicke model. It is demonstrated analytically by quantum mechanical derivation of the Lindblad equation for the Dicke model in the superradiant state coupled to Caldeira-Leggett thermal bath that the effective viscosity appearing in the semiclassical equations of motion of polaritonic condensate survives in the zero-temperature limit ...

Added: August 13, 2026

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Seidov S., Pugach N., Physical Review B: Condensed Matter and Materials Physics 2026

In this manuscript we consider a superconducting film in the vicinity of the critical temperature and presence of the proximity effect. We analytically solve the corresponding linearized Usadel equation and the self-consistency equation, defining the critical temperature. This is a system of coupled differential and integral equations for the anomalous Green's function and the order parameter of ...

Added: August 13, 2026

Generative geospatial modelling with geometric algebra

Yu Z., Wang J., Wang Z. et al., Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2026 Vol. 384 P. 1–16

The integration of data-driven and knowledge-driven approaches in generative geospatial modelling (GGM) is often hindered by their mathematical incompatibilities. Here, we propose a geometric algebra (GA)-based framework that employs a unified multi-vector representation to fuse heterogeneous data and diverse knowledge. The framework facilitates structured reasoning and hypothesis generation through a task-adaptable, five-stage cycle: representation, reasoning, ...

Added: August 13, 2026

Hadrons in N = 2 supersymmetric QCD from non-Abelian string on 2D black hole

Ievlev E., Marshakov A., Sumbatian G. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 Vol. 114 Article 046006

We continue the study of non-Abelian vortex string in 4D N =2 supersymmetric QCD (SQCD) as critical superstring, and extend this analysis to UðNÞ gauge theory with arbitrary even N and Nf = 2N number of quarks. We introduce a special mass deformation and show that the SQCD hadron spectrum is still given by the string spectrum on the ...

Added: August 13, 2026

Production of Λ hyperons in 4.0A GeV and 4.5A GeV carbon-nucleus interactions at the Nuclotron

Ratnikov F., Bocharnikov V., Journal of High Energy Physics 2026 Vol. 2026 P. 1–21

The BM@N experiment (Baryonic Matter at the Nuclotron) is the first fixed-target experiment at the JINR NICA accelerator complex. In this work, data on the interactions of a carbon-ion beam with kinetic energies of 4.0A GeV and 4.5A GeV with C, Al, Cu, and Pb targets are used to measure transverse momentum spectra and rapidity ...

Added: August 12, 2026

Hall effect in electrolyte solutions: Self-consistent Debye–Hückel–Onsager theory

Budkov Y., Kalikin N., Journal of Chemical Physics 2026 Vol. 165 Article 064506

A self-consistent statistical-mechanical theory of the Hall effect in electrolyte solutions is developed by extending the self-consistent Debye–Hückel–Onsager (SCDHO) framework to crossed electric and magnetic fields. The theory incorporates non-local ionic charge distributions via Slater-type form factors, regularizing the Coulomb interaction at short range, and accounts for dielectric friction through ion-specific coefficients, employing experimental values ...

Added: August 12, 2026

New bound on S1× S2-setting Bell locality of a nonseparable Werner state

Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.

In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...

Added: July 21, 2026