查看“︁ANNNI模型”︁的源代码

'''ANNNI模型'''全称轴向次近邻易辛模型，是一种[[统计力学]]模型，是[[易辛模型]]的变种。对于易辛模型晶格中每一个格点，在与其最近邻格点[[铁磁性]][[自旋]]相互作用的基础上，加入了与轴向次近邻格点的[[反铁磁性]]相互作用。这两种相互作用的竞争使得此模型在不同条件下呈现不同的[[相_(物质)|相]]。它是用于描述一些晶体中复杂的空间{{en-link|超结构|Superstructure (condensed matter)}}的最简易模型。

此模型最早在1961年由牛津大学的{{en-link|Roger Elliott|Roger Elliott (physicist)}}提出，用于描述[[铒]]晶体在低温下磁矩呈现的正弦有序相。<ref>{{cite journal
     |author = R. J. Elliott
     |year = 1961
     |title = Phenomenological discussion of magnetic ordering in the heavy rare-earth metals
     |url = https://archive.org/details/sim_physical-review_1961-10-15_124_2/page/n60
     |journal = Phys. Rev.
     |volume = 124
     |pages = 346&ndash;353
     |doi = 10.1103/PhysRev.124.346
 |bibcode = 1961PhRv..124..346E
     |issue = 2 }}</ref>不过'''ANNNI模型'''这个命名最早出现在1980年[[迈克尔·费希尔]]和{{en-link|Walter Selke}}的论文。<ref>{{cite journal
     |author = [[迈克尔·费希尔|M.E. Fisher]] and {{en-link|Walter Selke|Walter Selke|W. Selke}}
     |year = 1980
     |title = Infinitely many commensurate phases in a simple Ising model
     |journal = Phys. Rev. Lett.
     |volume = 44
     |pages = 1502&ndash;1505
     |doi = 10.1103/PhysRevLett.44.1502
|bibcode=1980PhRvL..44.1502F
     |issue = 23}}</ref>此模型为理解很多晶体磁性方面的实验结果提供了理论基础，包括[[磁铁]]，[[合金]]，[[吸附|吸附剂]]，[[同质异形体]]，{{en-link|多铁性体|Multiferroics}}等固体，<ref>{{cite journal
     |author = W. Selke
     |year = 1988
     |title = The ANNNI model—Theoretical analysis and experimental application
     |journal = Physics Reports
     |volume = 170
     |pages = 213&ndash;264
     |doi = 10.1016/0370-1573(88)90140-8
  |bibcode = 1988PhR...170..213S
     |issue = 4 }}</ref>
尤其是关于[[通约性|通约]]和不可通约的结构<ref>{{cite journal
     |author = {{en-link|Per Bak|Per Bak|P. Bak|}}
     |year = 1982
     |title = Commensurate phases, incommensurate phases, and the devil's staircase
     |journal = Reports on Progress in Physics
     |volume = 45
     |pages = 587&ndash;629
     |doi = 10.1088/0034-4885/45/6/001
  |bibcode = 1982RPPh...45..587B
     |issue = 6
     }}</ref>以及它们转化过程的相变。

==模型==

该模型的哈密顿量为

<math>
H = -J \sum_{\langle i, j \rangle} s_i s_j + \kappa J \sum_{[i, j]} s_i s_j
</math>

其中<math>\langle i, j \rangle</math>表示最近邻格点间的自旋相互作用，<math>[i, j]</math>表示轴向次近邻格点的相互作用，<math>J</math>是自旋相互作用得到强度，<math>\kappa \ge 0</math>是反铁磁性相对于铁磁性相互作用的强度。当<math>\kappa = 0</math>时该模型等价于易辛模型。

==参考资料==
{{reflist}}


[[Category:统计力学]]