Defining a critical temperature of a crossover from BEC to the normal phase

Abstract

We 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 [Formula: see text] 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 [Formula: see text] 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.