Rakhimov, A.Khudoyberdiev, A.Narzikulov, Z.Tanatar, Bilal2024-03-172024-03-172023-01-250217-9849https://hdl.handle.net/11693/114842We address the problem of identifying the critical temperature in a crossover from the Bose-Einstein condensed (BEC) phase to the normal phase. For this purpose we study the temperature dependence of magnetization of spin-gapped quantum magnets described by BEC of triplons. We have calculated the heat capacity CH at constant field and fluctuations in magnetization in a spin-gapped quantum magnet using the Hartree-Fock-Bogouliubov approximation and found optimized parameters of the Hamiltonian of triplon gas. In the region of phase transition, the heat capacity CH is smeared out due to the Dzyaloshinsky-Moriya (DM) interaction. The sharp maximum of the fluctuations in the magnetization is identified as the critical temperature of the crossover. © 2023 World Scientific Publishing Company.en-USCC BY 4.0 DEED (Attribution 4.0 International)https://creativecommons.org/licenses/by/4.0/Bose-Einstein condensation of triplonsExchange and Dzyaloshinsky-Moria anisotropyFluctuationsHeat capacityCrossoversArticle10.1142/S02179849225020621793-6640