AI 中文总结
研究人员通过费米子场方法，将二维 kagomé 晶格非均匀伊辛模型映射为非对称八顶点模型，推导了其热力学量与临界曲面，验证了其退化为低维伊辛模型时的精确结果。
AI 中文摘要
我们通过将二维非均匀伊辛模型（2DIM）映射到特定的非对称八顶点模型并构造对应的 R 矩阵，来研究 kagomé 晶格上的该模型。利用费米子表示，我们计算配分函数并推导主要热力学量的显式表达式。在热力学极限下，我们得到确定该模型相变的临界曲面的精确方程；还计算了铁磁情形下的自由能、比热和自发磁化强度。此外，我们证明当一个或两个耦合常数消失时，该模型分别退化为正方晶格和一维伊辛模型，在这两种极限下，我们的结果均复现了对应的精确临界耦合和自由能。
英文摘要
We investigate the two-dimensional inhomogeneous Ising model (2DIM) on the kagom'e lattice by mapping it onto a particular non-symmetric eight-vertex model and constructing the corresponding $R$-matrix. Using a fermionic representation, we evaluate the partition function and derive explicit expressions for the main thermodynamic quantities. In the thermodynamic limit, we obtain an exact equation for the critical surface determining the phase transition of the model. We also calculate the free energy, specific heat, and spontaneous magnetization in the ferromagnetic case. Furthermore, we show that when one or two coupling constants vanish, the model reduces, respectively, to the square-lattice and one-dimensional Ising models. In both limits, our results reproduce the corresponding exact critical couplings and free energies.
Comments31 pages, 4 figures
