钻石分形晶格上Ising模型的配分函数与关联函数

The partition function and correlation functions of the Ising model on a diamond fractal lattices

用参数变换方法,研究了钻石分形晶格上Ising自旋模型.精确求解了零场和非零场中系统的配分函数、自由能和关联函数,尤其推得了关联函数方程及其渐近行为的解析形式.结果表明,其关联行为与平移对称晶格上的Ising自旋系统类似.

With a diamond fractal lattice, the Ising model was exactly solved by parameter-transformation technique. The rigorous partition function, free energy and correlation functions were obtained for zero as well as non-zero field. In particular, an equation of cumulant pair correlation function and its analytical asymptotic expression was derived in the zero field. The result indicated that the correlation behaviors of the Ising model on a diamond fractal lattices are similar to the two-dimensional transitionally invariant lattices.