對(duì)伊辛模型的研究

摘  要：本文首先介紹了什么是伊辛模型及其提出的背景，接著介紹了布喇格—威廉斯近似方法，它是一種典型的平均場(chǎng)理論。雖然其存在缺陷，但可以說(shuō)明伊辛模型相變的主要特征。然后又簡(jiǎn)單介紹了用來(lái)討論臨界點(diǎn)性質(zhì)的臨界指數(shù)，最后通過(guò)對(duì)伊辛模型求嚴(yán)格解，得出了一維伊辛模型的局限性。

關(guān)鍵詞：伊辛模型   平均場(chǎng)   配分函數(shù)   相變

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   錄
0　引言……………………………………………………………………4
1　伊辛模型………………………………………………………………4
1．1 鐵磁體的伊辛模型 ………………………………………………4
1．2 其它模型的對(duì)照 …………………………………………………5
2　布喇格—威廉斯近似…………………………………………………6
2．１ 布喇格—威廉斯假設(shè)……………………………………………6
2．２ 配分函數(shù)…………………………………………………………7
2．３ 相變………………………………………………………………7
３　臨界指數(shù) ……………………………………………………………9
３．１ 臨界點(diǎn)的性質(zhì) …………………………………………………10
４　伊辛模型的嚴(yán)格解 …………………………………………………10
４．１ 一維伊辛模型的局限性 ………………………………………11
結(jié)束語(yǔ) ……………………………………………………………………13
參考文獻(xiàn) …………………………………………………………………14
致謝 ………………………………………………………………………15