Ground States And Thermal Properties Of The Blume-capel Model On The Antiferromagnetic Sawtooth Chain

The spin frustrated systems exhibit various intriguing ground states and thermodynamic properties and have been extensively studied in statistical mechanics and condensed matter physics. The antiferromagnetic sawtooth chain is one of the simple one dimensional structure of the spin frustrated systems. There is another parameter that may play a crucial role in their critical properties which is called single-ion anisotropy in Blume-Capel(BC) model, result in difference with Ising model. The present investigations was to study the ground states and thermodynamic properties of the antiferromagnetic spin-1 BC model on an infinite sawtooth chain in an external magnetic field by transfer matrix method. And studying the model is a great help to exploring the properties and physical mechanism of the corresponding real materials.The antiferromagnetic spin-1 BC model in an external magnetic field on the infinite sawtooth chain is solved exactly by using the transfer matrix method. We got the exact explicit expression of the free energy per site and then investigated ground states and thermodynamic properties of the model. First of all, we have got the exact expression for the total magnetization per site and investigated the properties of the magnetization as function of the external magnetic field for various values of the crystal field and for various values of the reduced temperature and as a function of the temperature for various values of the external magnetic field and for various values of the crystal field. The model exhibits the formation of magnetization plateaus for low temperatures, and it is shown that their properties depend strongly on the sign and strength of the crystal field. For various values of the external magnetic field and for various values of the crystal field, with the decrease of the temperature, the curves of the magnetization exhibit convergence. In the limit T?0 the magnetization can acquire onlu a few possible value which correspond to the possible ground states of the model. By the properties of low temperatures magnetization plateaus, all possible long range order ground states of the model are found and discussed. The existence of nontrivial singular ground states is proven and exact explicit expressions for them are found by calculating the T?0 limit magnetization. The macroscopic degeneracies of ground states are studied by calculation of the T?0 limit entropy. The entropy of all plateaulike ground states is zero, i.e., all of them have finite degeneracies and the entropy of all singular ground states is nonzero, i.e., all the singular ground states have infinite macroscopic degeneracies. Then, the magnetocaloric properties of the model is studied. The model is found to display qualitatively different behaviordepending on the sign of the single-ion anisotropy D. For nonnegative values of D we observe negative isothermal entropy changes, i.e., the sample heats up when the external magnetic field is applied adiabatically; On the contrary, if D is negative the entropy changes are solely positive and it cools down when the external magnetic field is applied adiabatically. At last, temperature variations of the susceptibility and the specific heat are explored in detail. Temperature variations of the susceptibility in magnetization plateaus has maximum, while it is monotone decreasing at singular ground states. The temperature dependence of the specific heat has only one round maximum at the singular ground states and in the regions far away from the singular ground states while a more shrinking double-peak temperature dependence can be detected in the vicinity of the singular ground states. The additional low-temperature peak moves towards lower temperatures upon nearing the singular ground state of the external magnetic field until it completely vanishes at the point of the singular ground state.