The Spin-Wave Study On One-Dimensional Ferromagnetic Model With Next-Nearest Neighbor Interaction

In this thesis, we apply the modified spin-wave theory within the simple self-consistent method to study the low-temperature properties of the XY and Heisenberg ferromagnetic chain considering the next-nearest neighbor interaction. We focus on how the next-nearest neighbor interaction affects the internal energy, specific heat and susceptibility etc..The paper has four chapters. The first chapter introduces the background, the content, the method of the models and the development of the models.In Chapter 2, we apply the modified spin-wave theory to the one-dimensional spin-1/2 ferromagnetic XY model with the next-nearest neighbor interaction. The thermodynamic divergences which the conventional spin-wave theory encounters with, are solved by implementing Takahashi's idea through introducing a Lagrange multiplier in the Hamiltonian to keep zero magnetization, thus, we can study how the next-nearest neighbor interaction affects the states. It is shown that the next-nearest neighbor interaction has an influence on the ground-state and low-temperature properties of the system. The exponential laws which are induced by the next-nearest neighbor interaction, are found for heights of maxima of the specific heat and its coefficient, as well as the maximum and minimum of the susceptibility coefficient. The maximum positions of the specific heat and its coefficient fit well to the linear and exponential laws under the next-nearest neighbor interaction, respectively.In Chapter 3, the modified spin-wave theory is still applied to the one-dimensional spin-1/2 ferromagnetic Heisenberg model with the next-nearest neighbor interaction.The influence of the next-nearest neighbor interaction on the thermodynamic properties of the system, is obtained within the self-consistent method. The exponential and linear laws which are induced by the next-nearest neighbor interaction, are found for heights and positions of maxima of the specific heat, respectively. At positions of the specific heat maximum, the magnetic susceptibility, as well as the internal energy and free energy,exhibit the linear decrease with the next-nearest neighbor interaction, but the entropy has an exponential decrease. Unlike the XY model, when handling the internal energy,we consider a higher order which makes the result well agreement to the Bethe-Ansatz data in the case without next-nearest neighbor interaction.Chapter 4 will give a brief summary.