【作者】 许玲；

【导师】 晏世雷；

【作者基本信息】 苏州大学 ， 理论物理， 2007， 硕士

【摘要】 本文在有效场理论和切断近似框架内,研究自旋S=1的随机横向单轴与双轴晶场Ising模型的临界性质和磁化。首先分别选择二维方格子及三维简立方格子,研究横向随机晶场Ising模型的相图和磁化行为,重点是横向随机晶场浓度和晶场比率对相图和磁化的影响。给出了T - Dx空间的相图和m - T空间的磁化图。在晶场稀疏情况下,负晶场方向存在临界温度的峰值,正方向可出现重入现象。晶场比率取+0.5和-0.5时,磁有序相范围缩小,特别是晶场比率取-0.5时,随晶场浓度的降低,临界温度峰值从横向晶场负方向渡越到正方向。固定某一负晶场值,不同晶场比率的磁化行为有明显差异。同时高温和低温下的磁化也存在许多差异。其次,研究了对于简立方晶格,纵向及横向双轴晶场Ising模型的临界性质。仅稀疏横向晶场时,讨论了T - Dx和T - Dz空间的三临界点和它的轨迹。在T - Dx空间内发现了两个三临界点的新现象。一条二级相变线存在于两条一级相变线之间,由两个三临界点隔开。稀疏浓度的变化导致了三临界点轨迹的一个复杂的关联。改变纵向晶场,基态出现简并。在T - Dz空间内,随着横向晶场浓度的降低,标正(负) Dx /J值的相变线的有序相范围变大(小)。同时在T - Dz空间同时稀疏时纵向晶场和横向晶场,发现当横向晶场浓度减小时,三临界点能够存在的纵向晶场浓度范围也将减小。在此情况下,正负方向横向晶场作用下系统的临界行为有所不同:当横向晶场取正方向时,在一定纵向晶场稀疏浓度范围内出现双三临界点;而横向晶场取负方向时,仅存在一个三临界点。更多还原

【Abstract】 Within the framework of the effective field theory (EFT) and cutting approximation, critical properties of spin-1 transverse random crystal field Ising model and biaxial Ising model with both longitudinal crystal field and transverse crystal field are investigated.Firstly, we study the phase diagrams and magnetization behaviors of transverse random crystal field Ising model for square lattice and simple cubic lattice respectively. We discuss in detail the influence of transverse random crystal field concentration and crystal field ratio on the phase diagrams and magnetization behaviors. We give phase diagrams in T - Dx space and magnetization curves in m - T space. Under crystal field dilution condition, there exists the peak value of critical temperature in the direction of negative crystal field and reentrant phenomena in the direction positive critical field. While choosing crystal field ratioα=+0.5 andα=-0.5, the range of magnetic ordered phase shrinks. In particular, we find that, with decreasing of concentration, the peak value of critical temperature undergoes a crossover from negative to positive direction of transverse crystal field when the ratioα=-0.5. The magnetization behaviors have apparent differences for a given negative crystal field value when the crystal field ratio is different. The magnetizations have a lot of differences at high and low temperatures.Secondly, critical properties of biaxial Ising model with both longitudinal crystal field and transverse crystal field are investigated for a simple cubic lattice. When transverse crystal field is diluted, the tricritical point (TCP) and its trajectory are discussed in T - Dx and T - Dz space. A new phenomenon of two TCPs is found in T - Dx space. There exists a second-order line between two first-order lines, separated by two TCPs. The change of dilution concentration leads to a complex relation of trajectory of the TCP. The degenerate patterns at ground state appear by changing longitudinal crystal field. The range of ordered phase for transition lines labeled positive or (negative) value of Dx / J becomes larger or (smaller) with the decrease of t x in T - Dz space. When longitudinal crystal field and transverse crystal field are diluted simultaneously in T - Dz space, we reduce the dilution concentration of transverse crystal field and find that the dilution concentration range of longitudinal crystal field to maintain TCP’s existence is decreased. In this case, the system shows different behaviors while choosing positive or negative transverse crystal field. When transverse crystal field is positive, double TCPs appear in certain dilution concentration range of longitudinal crystal field. However, there exists only one TCP when transverse crystal field is negative.更多还原