Exactly Solution Of The Spin-1/2 Anti-ferromagnetic Ising Model On The Diamond Chain

Diamond chain model is one of the important theoretical model in condensed matter physics which is a quasi one-dimensional lattice spin system. Theoretical researches about it come out in unending flow, different forms of diamond chain compounds which are closely related to experiments have aroused people’s wide attention in last decades. In this thesis with transfer matrix method we studied the classical infinite Ising anti-ferromagnetic diamond chain.The anti-ferromagnetic Ising model with multisite interaction on an infinite diamond chain in an external magnetic field is solved exactly by using the transfer matrix method.We got the exact explicit expression of the free energy per site and further obtained the analytical form for magnetization, specific heat, magnetic susceptibility. First we got the magnetization curves for low temperature under the action of external magnetic field,founding that the magnetization curves exhibit the behavior of platforms and with increasing of the temperature the platforms gradually disappear. Also we found the behavior of magnetization platforms are closely associated with ?(the ratio of multisite interaction parameter with the nearest neighbor interaction parameter). There are five platforms when ? ?0, with the increasing of ?, the number and the length of the platforms changed significantly. Through the analysis of the magnetization platforms when T ?0 we got the possible spin configurations of the system and calculated the corresponding ground state energy, at last we got the ground states phase diagram of the system. Seeing from the diagram there are five long-range order ground states(saturated ground states and various platforms), the corresponding magnetization values are m ?0,?0.5,?1. The singular ground states which corresponding to the discontinuities between the magnetization platforms appear at the adjacent long range order ground states.For the magnetization platforms phenomenon of the system when the temperature approaching zero it can be concluded that the lattice spins are tending to be arranged along the external magnetic field direction with the magnetization equal to m? ?1. With the decreasing of the magnetic field it is because ? that make the structure of the platforms changed significantly and the magnetization curves display a strict magnetization jump between the platforms. With the rising temperature the influence of thermal fluctuation on the system become obvious which causing the interaction between the spins becoming weaker and weaker so that the system tends to a state of disorder and the magnetizationplatforms gradually disappear.At last we got and analysed detailedly about the magnetic susceptibility and the specific heat properties of the system at the singular ground states or the vicinity near them.Founding that the magnetic susceptibility present peak values in magnetization plateaus area while it is monotone decreasing at singular ground states with the decreasing of temperature. The product of temperature and susceptibility TkB? tend to zero when the magnetization are in magnetization platforms area at T?0, while they trend to a nonzero constant at singular ground states. Through the analysis of the curves which the specific heat change along with temperature when ? ?0, 0.5, we found that there is a single peak behavior at singular ground states or in the regions far away from them( where corresponding to different field values) but a double-peak behavior appear at the vicinity of the singular ground states. The phenomenon is more obvious when the system does not contain multi-body interaction, namely,? ?0.