论文标题
分区函数的配方和有限晶格位点的二维最近邻居Ising模型的磁化
Formulation of the partition functions and magnetization for two-dimensional nearest neighbour Ising models for finite and infinite lattice sites
论文作者
论文摘要
使用组合方法，在磁场存在的情况下，已为16个位点的平方晶格得出了二维最近邻居Ising模型的分区函数。已经提出了一种对所有位置排列的所有配置枚举的新型分层方法。该枚举是通过对适当图的系统分析执行的，而无需采用任何算法方法或计算工具。然后，在磁场和最近的邻居相互作用能量方面，所得的代数EQN可以提供一种方法来推论无限位点热力学极限中的磁化。提出了用于非零磁场的半经验等式用于磁化。
Using a combinatorial method, the partition functions for two-dimensional nearest neighbour Ising models have been derived for a square lattice of 16 sites in the presence of the magnetic field. A novel hierarchical method of enumeration of all the configurations for any arrangement of sites has been proposed. This enumeration has been executed by a systematic analysis of the appropriate diagrams without employing any algorithmic approach or computational tools. The resulting algebraic eqn in terms of the magnetic field and nearest neighbour interaction energies may then provide a methodology for deducing the magnetization in the thermodynamic limit of infinite sites. A semi-empirical eqn for magnetization is proposed for non-zero magnetic fields.
