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Progress of Theoretical Physics

Thermal Properties of the System of Magnetic Bosons: -- Bose-Einstein Ferromagnetism --

Keiji Yamada

Published Feb 1, 1982• 32 citations

Abstract

Thermal and magnetic properties of the system of ideal magnetic bosons exposed to a magnetic field are investigated. The Boson particle is assumed to have a spin of magnitude one and a magnetic moment m0. The results are summarized as follows: The grand thermodynamical potential of the system has a certain singularity on the field versus temperature (T-H) plane, in which two sorts of singular lines SL1 and SL3 as shown in Fig. 1 appear. The Bose-Einstein (BE) condensation occurs in a lower temperature and higher field region bounded by the line SL3 or ACB on the T-H plane. A spontaneous magnetization appears below a critical temperature, at which the zero field susceptibility diverges. This nature is called the “BE Ferromagnetism” in this paper. The system exhibits a phase transition of first order on the line SL1 and that of third order on SL3. The transition reduces to the second order one at the critical temperature T0. The critical exponents at T0 are found to be α = α′ = 0, β = γ = 1 and δ = 2, which satisfy the Griffiths inequalities. In conclusion, the system of magnetic bosons which can really exist is also discussed.

DOI: 10.1143/ptp.67.443

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Thermal and magnetic properties of the system of ideal magnetic bosons exposed to a magnetic field are investigated. The Boson particle is assumed to have a spin of magnitude one and a magnetic moment m0. The results are summarized as follows: The grand thermodynamical potential of the system has a certain singularity on the field versus temperature (T-H) plane, in which two sorts of singular lines SL1 and SL3 as shown in Fig. 1 appear. The Bose-Einstein (BE) condensation occurs in a lower temperature and higher field region bounded by the line SL3 or ACB on the T-H plane. A spontaneous magnetization appears below a critical temperature, at which the zero field susceptibility diverges. This nature is called the “BE Ferromagnetism” in this paper. The system exhibits a phase transition of first order on the line SL1 and that of third order on SL3. The transition reduces to the second order one at the critical temperature T0. The critical exponents at T0 are found to be α = α′ = 0, β = γ = 1 and δ = 2, which satisfy the Griffiths inequalities. In conclusion, the system of magnetic bosons which can really exist is also discussed.

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We investigate the thermodynamics of a spin-1 Bose gas with fixed magnetization including the quadratic Zeeman energy shift. Our calculations are based on the grand canonical description for the ideal gas and the classical field approximation for atoms with ferromagnetic and antiferromagnetic interactions. We confirm the occurrence of a double phase transition in the system that takes place due to two global constraints. We show analytically for the ideal gas how critical temperatures and condensed fractions are changed by a nonzero magnetic field. The interaction strongly affects the condensate scenario below the second critical temperature. The effect imposed by interaction energies becomes diminished in high magnetic fields where condensation of both ferromagnetic and antiferromagnetic atoms agrees with the ideal gas results.

Thermodynamics of a spin-1 Bose gas with ferromagnetic interactions is investigated via the mean-field theory. It is apparently shown in the specific-heat curve that the system undergoes two phase transitions, the ferromagnetic transition and Bose-Einstein condensation, with the Curie point above the condensation temperature. Above the Curie point, the susceptibility fits the Curie-Weiss law perfectly. At a fixed temperature, the reciprocal susceptibility is also in a good linear relationship with the ferromagnetic interaction.

Abstract We study the thermodynamic properties of a neutral vector boson gas in presence of a constant magnetic field, by means of a semi-classical approach that allows to introduce the spin in the non-relativistic spectrum of the bosons. Bose-Einstein condensation is obtained and it turns out to depend on all the parameters involved in the problem: temperature, particle density and magnetic field. A spontaneous magnetization appears at low temperature as a consequence of the condensed state. The axial symmetry imposed in the system by the magnetic field presence, splits the pressure in two components, one along and another perpendicular to the magnetic axis. Under certain conditions, the perpendicular pressure becomes negative signaling that the system undergoes a transversal magnetic collapse. The spontaneous magnetization might be useful to model magnetic field production inside compact stars, while the negative pressures imposes certain limits to the temperatures and densities needed inside these objects to support a given magnetic field.

The magnetic properties of charged vector boson gas are studied in the very weak, and very strong (near critical value) external magnetic field limits. When the density of the vector boson gas is low, or when the external field is strong, no true Bose–Einstein condensation occurs, though significant amount of bosons will accumulate in the ground state. The gas is ferromagnetic in nature at low temperature. However, Bose–Einstein condensation of vector bosons (scalar bosons as well) is likely to occur in the presence of a uniform weak magnetic field when the gas density is sufficiently high. A transitional density depending on the magnetic field seems to exist below which the vector boson gas changes its property with respect to the Bose–Einstein condensation in a uniform magnetic field.

Thermodynamical properties of an interacting boson system at finite temperatures and zero chemical potential are studied within the framework of the Skyrme-like mean-field toy model. It is assumed that the mean field contains both attractive and repulsive terms. Self-consistency relations between the mean field and thermodynamic functions are derived. It is shown that, for sufficiently strong attractive interactions, this system develops a first-order phase transition via the formation of a Bose condensate. An interesting prediction of the model is that the condensed phase is characterized by a constant total density of particles. It is shown that the energy density exhibits a jump at the critical temperature.