The Thermodynamic Properties Of Quasione-Dimensional Magnetic System

The ground state properties and the low temperature thermodynamic properties in several different quasi one-dimensional quantum magnetic systems were studied in the present thesis. We put our emphases on four sections: the opening of the energy gap and its effects on the thermodynamic properties in low temperature, quantum fluctuation and the hidden long-distance order parameters, the magnetization and the specific heat properties under the extern magnetic field of the ferromagnetic chain, and the energy spectrum of the ferromagnetic ladder. The paper is arranged as five chapters:In the first chapter, we give a general introduction and summation of the current study background and states in the quasi one-dimensional magnetic systems. The method and some simple and important results are presented.In the second chapter, we study the ground state energy gap and the spin-Peierls phase transition in the quasi one-dimensional spin=l/2 dimerized anti-ferromagnetic single chain. We find it has the same behavior as that of the continuous phase transition in BCS super-conduction theory: the nonzero ground state energy gap decreases to zero at the finite critical temperature Tsp, and the specific heat takes on divergence. These quantum characters are indeed observed on many experiments.In the third chapter, the effects on the properties of ground state of spin=1 anti-ferromagnetic single chain, from dimerization, exchange anisotropy and single-ion anisotropy, are investigated. We find these three different actions have similar effects: they all can divide the system into two different phases, which can be described by two different order parameters respectively. Beyond this, we still investigate the quantum fluctuation in the system.In the forth chapter, we study the behavior of magnetization and the specific heat in the ferromagnetic XXZ chain under external magnetic field. From the investigation on the effects of exchange anisotropy, we can see that exchange anisotropy exert a strong effect tothe order in the system. Under the weak external magnetic field, the formed long-distance order in the system relate to both the external magnetic field and exchange anisotropy.In the chapter five, we study the quasi particle excitation energy spectrum and corresponding energy gap in ferromagnetic (1/2, 1) tow-leg Heisenberg ladder system. We prove the general characters of gapped system in low temperatures again: near zero temperature, the specific heat and uniform susceptibility take on exponent behavior.On specific conditions, our above theoretical results can return to that of precursor. And also on general conditions, we derived meaningful and novel results, which provide good reasons for some low temperature experimental phenomena.