O(N)模型

在統計力學中，O(n)模型是易辛模型的推廣，它描述了晶格的自旋。^[1]

H=-J{\sum }_{\langle i,j\rangle }\mathbf {s} _{i}\cdot \mathbf {s} _{j}

$\mathbf {s} _{i}\in R^{n}$ ， $\langle i,j\rangle$ 代表晶格上每一對相鄰的格子。

場論

$F(\phi )=\int d^{d}x{\frac {1}{2}}(\partial \phi )^{2}+{\frac {m^{2}}{2}}\phi ^{2}+g(\phi ^{2})^{2}+\ldots$

$(\partial \phi )^{2}=\sum _{i,a}(\partial _{i}\phi _{a})^{2}$

$\phi =(\phi _{1},\ldots ,\phi _{N})$

n=0

n=1

n=2

n=3

n=4

玻茨模型也描述其他易辛模型的推廣。

^ Stanley, H. E. Dependence of Critical Properties upon Dimensionality of Spins. Phys. Rev. Lett. 1968, 20: 589–592. Bibcode:1968PhRvL..20..589S. doi:10.1103/PhysRevLett.20.589.
^ de Gennes, P. G. Exponents for the excluded volume problem as derived by the Wilson method. Phys. Lett. A. 1972, 38: 339–340. Bibcode:1972PhLA...38..339D. doi:10.1016/0375-9601(72)90149-1.
^ Gaspari, George; Rudnick, Joseph. n-vector model in the limit n→0 and the statistics of linear polymer systems: A Ginzburg–Landau theory. Phys. Rev. B. 1986, 33: 3295–3305. Bibcode:1986PhRvB..33.3295G. doi:10.1103/PhysRevB.33.3295.

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