Spherically symmetric approaches in the low-dimensional magnetism theory

A.F. Barabanov^a, V.E. Valiulin^b, c, A.V. Mikheyenkov^†^b, c, P.S. Savchenkov^d, e
^aInstitute for High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse 14, Troitsk, Moscow, 108840, Russian Federation
^bVereshchagin Institute for High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse 14, Troitsk, Moscow, 108840, Russian Federation
^cMoscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141701, Russian Federation
^dNational Research Centre ‘Kurchatov Institute’, pl. akad. Kurchatova 1, Moscow, 123182, Russian Federation
^eNational Research Nuclear University ‘MEPhI’, Kashirskoe shosse 31, Moscow, 115409, Russian Federation

The main ideas and the most important results of the spherically symmetric self-consistent approach and a number of related theoretical algorithms are presented. These methods make it possible to study low-dimensional Heisenberg-type spin models, including frustrated ones, with careful consideration of the theoretic (Mermin—Wagner and Marshall) theorems, as well as the site spin constraint. Thus, the difficulties that may arise in the traditional analysis of low-dimensional magnetic systems are avoided. The approach can also be applied to the spin-pseudospin model, and is also embedded in more complex constructions when considering spin models with free carriers, such as the basic and three-band Hubbard models, t — J and s — d models, and the Kondo lattice.

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Keywords: low-dimensional magnetism, multi-exchange Heisenberg model, frustration, spherically symmetric approach
PACS: 75.10.Jm, 74.72.−h, 75.30.Kz, 75.50.Ee, 75.50.Gg, 75.70.Tj (all)
DOI: 10.3367/UFNe.2025.06.039948
URL: https://ufn.ru/en/articles/2026/2/b/
Citation: Barabanov A F, Valiulin V E, Mikheyenkov A V, Savchenkov P S "Spherically symmetric approaches in the low-dimensional magnetism theory" Phys. Usp. 69 (2) (2026)

Received: 11th, April 2025, revised: 8th, June 2025, accepted: 15th, June 2025

Оригинал: Барабанов А Ф, Валиулин В Э, Михеенков А В, Савченков П С «Сферически-симметричные подходы в теоретическом исследовании низкоразмерных магнетиков» УФН 196 125–148 (2026); DOI: 10.3367/UFNr.2025.06.039948

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