对伊辛模型的研究.doc

对伊辛模型的研究

摘  要：本文首先介绍了什么是伊辛模型及其提出的背景，接着介绍了布喇格—威廉斯近似方法，它是一种典型的平均场理论。虽然其存在缺陷，但可以说明伊辛模型相变的主要特征。然后又简单介绍了用来讨论临界点性质的临界指数，最后通过对伊辛模型求严格解，得出了一维伊辛模型的局限性。

关键词：伊辛模型   平均场   配分函数   相变

Abstract: This article first introduced any is the background which the Ising model and proposed, then it introduced the Bragg - Williams approximate method, it is one kind of typical average field theory. Although its existence flaw, may explain the Ising model changes main characteristic. Then it simple introduced the critical exponent , which used for to discuss the critical point nature, finally we got the result of the Ising model’s limitations from the Ising model’s strict solution.

Keywords: Ising model ； average field ； partition function ；  phase transformation.

目   录
0　引言……………………………………………………………………4
1　伊辛模型………………………………………………………………4
1．1 铁磁体的伊辛模型 ………………………………………………4
1．2 其它模型的对照 …………………………………………………5
2　布喇格—威廉斯近似…………………………………………………6
2．１ 布喇格—威廉斯假设……………………………………………6
2．２ 配分函数…………………………………………………………7
2．３ 相变………………………………………………………………7
３　临界指数 ……………………………………………………………9
３．１ 临界点的性质 …………………………………………………10
４　伊辛模型的严格解 …………………………………………………10
４．１ 一维伊辛模型的局限性 ………………………………………11
结束语 ……………………………………………………………………13
参考文献 …………………………………………………………………14
致谢 ………………………………………………………………………15