查看“︁O(N)模型”︁的源代码

在[[统计力学]]中，'''O(''n'')模型'''是易辛模型的推广，它描述了[[晶体结构|晶格]]的[[自旋]]。<ref>{{Cite journal|title=Dependence of Critical Properties upon Dimensionality of Spins|last=Stanley|first=H. E.|journal=Phys. Rev. Lett.|doi=10.1103/PhysRevLett.20.589|year=1968|volume=20|pages=589–592|bibcode=1968PhRvL..20..589S}}</ref> 

[[哈密顿力学|哈密顿量]]是

: <math>H = -J{\sum}_{\langle i,j \rangle}\mathbf{s}_i \cdot \mathbf{s}_j</math>

<math>\mathbf{s}_i \in R^n</math>，<math>\langle i, j \rangle</math>代表[[晶格]]上每一对相邻的[[格点|格子]]。

== 场论 ==
<math>F(\phi) = \int d^d x \frac{1}{2}(\partial \phi)^2 + \frac{m^2}{2}\phi^2 + g(\phi^2)^2 + \ldots</math>

<math>(\partial \phi)^2 = \sum_{i, a}( \partial_i \phi_a)^2</math>

<math>\phi = (\phi_1, \ldots, \phi_N)</math>

== 舉例 ==

: <math>n=0</math>：[[自避行走]]<ref>{{Cite journal|title=Exponents for the excluded volume problem as derived by the Wilson method|last=de Gennes|first=P. G.|journal=Phys. Lett. A|doi=10.1016/0375-9601(72)90149-1|year=1972|volume=38|pages=339–340|bibcode=1972PhLA...38..339D}}</ref><ref>{{Cite journal|title=n-vector model in the limit n→0 and the statistics of linear polymer systems: A Ginzburg–Landau theory|last=Gaspari|first=George|last2=Rudnick|first2=Joseph|journal=Phys. Rev. B|doi=10.1103/PhysRevB.33.3295|year=1986|volume=33|pages=3295–3305|bibcode=1986PhRvB..33.3295G}}</ref>
: <math>n=1</math>：[[易辛模型]]
: <math>n=2</math>：[[XY模型]]
: <math>n=3</math>：[[海森堡模型]]
: <math>n=4</math>：[[标准模型]]中[[希格斯场]]的[[玩具模型]]

[[玻茨模型]]也描述其他易辛模型的推广。

== 相关條目 ==
* [[大N展开]]
* [[Mermin–Wagner定理]]
* [[杨米尔斯场论]]

== 阅读 ==
* Peskin, Schroeder. Intro QFT.
* David Tong. Statistical Field Theory.
* https://katzgraber.org/teaching/SS07/files/kay.pdf{{Wayback|url=https://katzgraber.org/teaching/SS07/files/kay.pdf |date=20160309043613 }}

== 参考文献 ==
{{Reflist}}

{{Quantum field theory}}
{{String theory}}
[[Category:量子场论]]
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