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Спиновые модели с динамически изменяемой геометрией
С. 46–47.
Загвоздина К. О.
Publication based on the results of:
In book
М.: МИЭМ НИУ ВШЭ, 2019.
D.D. Sukhoverkhova, L.N. Shchur, , in: Параллельные вычислительные технологии – XIX всероссийская конференция с международным участием, ПаВТ'2025. Короткие статьи и описания плакатов.: Издательский центр ЮУрГУ, 2025. P. 82–89.
We apply supervised deep machine learning techniques to extract properties of the anisotropic Ising model. We consider two cases of anisotropy: orthogonal and diagonal. From the predictions of the neural network, we obtained phase probability functions, from which we measured two quantities: the critical temperature and the critical exponent of the correlation length. We estimated ...
Added: December 4, 2025
Skopenkov M., Ustinov A., Zaslavsky A., , in: Mathematics via Problems: Part 3: Combinatorics* 3: Combinatorics.: Providence: AMS, 2023.
Added: October 16, 2025
Заславский А. А., Skopenkov M., Ustinov A., В кн.: Элементы математики в задачах: через олимпиады и кружки—к профессии.: М.: МЦНМО, 2018.
The chapter is devoted to random walks and electrical networks. ...
Added: October 13, 2025
Баранов Д. В., Skopenkov M., Ustinov A., Математическое просвещение 2011 № 15 С. 229–230
This collection of problems is based on the project “Random walks and electric circuits” of the XXII Summer Conference of the Tournament of Cities and problem 14.12 from the problem book “Mathematical Enlightenment” (issue 14, p. 274). ...
Added: October 9, 2025
Skopenkov M., Смыкалов В., Ustinov A., Математическое просвещение 2012 № 16 С. 25–47
The article is devoted to the mathematical theory of electrical networks. ...
Added: October 9, 2025
Chertenkov V., Shchur L., Lecture Notes in Computer Science 2025 Vol. 15406 P. 434–449
Machine learning is a new tool for investigating physical models. One possible applications is the study of phase transitions analyzing the distribution of spins on regular lattices using supervised learning approach. A new question is the applicability of transfer learning, a network supervised on a particular model and used to infer information about another model.
The ...
Added: February 10, 2025
D. D. Sukhoverkhova, L. N. Shchur, Lobachevskii Journal of Mathematics 2025 Vol. 46 No. 1 P. 528–534
We investigate the possibility of extracting features of second-order phase transitions using transfer machine learning. We have performed supervised machine learning for binary classification of snapshots of the spin distribution of the isotropic Ising model. The binary classification is performed in ferromagnetic and paramagnetic phases using a known critical temperature. The trained network is used ...
Added: January 13, 2025
Danilov V., Михайлова С. О., Математические заметки 2024 Т. 116 № 6 С. 881–897
В этой статье на примере случайных блужданий будет представлен метод решения параболических задач на сетке. Ввиду стохастических свойств случайных блужданий ранее полученные интерполяционные методы решения гиперболических задач (преобразование Фурье, теорема В. А. Котельникова) на сетках неприменимы. В данной статье строится формальная асимптотика фундаментального решения задачи Коши и краевых задач для параболического случайного блуждания по решетке, ...
Added: November 26, 2024
Influence of anisotropy on the study of critical behavior of spin models by machine learning methods
Sukhoverkhova D., Shchur L., / Series arXiv "math". 2024. No. 2410.14523.
In this paper, we applied a deep neural network to study the issue of knowledge transferability between statistical mechanics models. The following computer experiment was conducted. A convolutional neural network was trained to solve the problem of binary classification of snapshots of the Ising model's spin configuration on a two-dimensional lattice. During testing, snapshots of ...
Added: October 21, 2024
Sukhoverkhova D., Shchur L., Письма в Журнал экспериментальной и теоретической физики 2024 Т. 120 № 8 С. 644–649
In this paper, we applied a deep neural network to study the issue of knowledge transferability between statistical mechanics models. The following computer experiment was conducted. A convolutional neural network was trained to solve the problem of binary classification of snapshots of snapshots of the location of spins of the Ising model on a two-dimensional ...
Added: September 25, 2024
Leonidov A., Antonov A., Semenov A. G., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2023 Vol. 108 No. 2 Article 024134
Transitions between metastable equilibria in the low-temperature phase of dynamical Ising game with activity spillover are studied in the infinite time limit. It is shown that exponential enhancement due to activity spillover, which takes place in finite-time transitions, is absent in the infinite time limit. In order to demonstrate that, the analytical description for infinite ...
Added: March 16, 2024
Aladyshkin A. Y., Фраерман А. А., Н. Новгород: Национальный исследовательский Нижегородский государственный университет им. Н.И. Лобачевского, 2024.
В книге затронут широкий круг вопросов физики ограниченных твёрдых тел. Рассмотрено взаимодействие электромагнитного излучения рентгеновского диапазона, «тепловых» нейтронов и электронов с поверхностью твёрдого тела и многослойными структурами. Излагаются основы теории электронных состояний в полуограниченных твёрдых телах и применение метода туннельной спектроскопии для экспериментального изучения этих состояний. Возникновение поверхностной (прикраевой) сверхпроводимости на границах раздела рассматривается как ...
Added: February 1, 2024
Konakov V., Menozzi S., / Series arXiv "math". 2023. No. 2312.06222.
Abstract. We prove central and local limit theorems for random walks on the Poincar´e hyperbolic space of
dimension n ě 2. To this end we use the ball model and describe the walk therein through the M¨obius addition
and multiplication. This also allows to derive a corresponding law of large numbers. ...
Added: December 12, 2023
Diana Sukhoverhova, Chertenkov V., Burovskiy E. et al., Lecture Notes in Computer Science 2023 Vol. 14389 P. 314–329
We analyze the Ising model and the Baxter-Wu model in two dimensions using deep learning networks trained to classify paramagnetic (PM) and ferromagnetic (FM) phases. We use the usual Metropolis Monte Carlo algorithm to create uncorrelated snapshots of spin states. The images used as training data are labeled as belonging to the PM state or ...
Added: November 9, 2023
Molchanov S., Куценко В. А., Яровая Е. Б., Успехи математических наук 2023 Т. 78 № 5(473) С. 181–182
Условия надкритичности для ветвящихся блужданий в случайной убивающей среде с единственным центром размножения. ...
Added: November 3, 2023
Budkov Y., Брандышев П. Е., Journal of Chemical Physics 2023 Vol. 159 No. 17 Article 174103
Based on the variational field theory framework, we extend our previous mean-field formalism [Y. A. Budkov and A. L. Kolesnikov, JStatMech 2022, 053205.2022], taking into account the electrostatic correlations of the ions. We employ a general covariant approach and derive a total stress tensor that considers the electrostatic correlations of ions. This is accomplished through an ...
Added: November 2, 2023
Chertenkov V., Burovskiy E., Shchur L., , in: Supercomputing: 8th Russian Supercomputing Days, RuSCDays 2022, Moscow, Russia, September 26–27, 2022, Revised Selected PapersVol. 13708.: Springer, 2022. P. 397–408.
We explore the possibilities of using neural networks to study phase transitions. The main question is the level of accuracy which can be achieved for the estimates of the critical point and critical exponents of statistical physics models. We generate data for two spin models in two dimensions for which analytical solutions exist, the Ising ...
Added: March 31, 2023
Bogoslovskiy N. A., Петров П. В., Аверкиев Н. С., Письма в Журнал экспериментальной и теоретической физики 2021 Т. 114 № 5-6(9) С. 383–390
A model of an impurity system in semiconductors consisting of spins randomly distributed in space with a hydrogen-like distance dependence of the exchange energy in the Ising Hamiltonian has been studied. The distribution function of the exchange energy and the mean square of the magnetic moment have been calculated as functions of the concentration. It ...
Added: November 8, 2022
М. Б. Скопенков, А. В. Устинов, Успехи математических наук 2022 Т. 77 № 3(465) С. 73–160
We survey and develop the most elementary model of electron motion introduced by R.Feynman. In this game, a checker moves on a checkerboard by simple rules, and we count the turns. Feynman checkers are also known as a one-dimensional quantum walk or an Ising model at imaginary temperature. We solve mathematically a problem by R.Feynman ...
Added: August 12, 2022
Faizullina Kamilla, Pchelintsev Ilya, Burovskiy E., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2021 Vol. 104 Article 054501
We study a lattice model of a single magnetic polymer chain, where Ising spins are located on the sites of a lattice self-avoiding walk in $d=2$. We consider the regime where both conformations and magnetic degrees of freedom are dynamic, thus the Ising model is defined on a dynamic lattice and conformations generate an annealed disorder. Using Monte Carlo ...
Added: November 5, 2021