We study the three-state antiferromagnetic Potts model on the simple-cubic lattice, paying attention to the surface critical behaviors. When the nearest-neighboring interactions of the surface is tuned, we obtain a phase diagram similar to the XY model, owing to the emergent O(2) symmetry of the bulk critical point. For the ordinary transition, we get $y_{h1}=0.780\left(3\right), {\eta }_{\parallel }=1.44\left(1\right)$, and ${\eta }_{\perp }=0.736\left(6\right)$; for the special transition, we get $y_s=0.59\left(1\right), y_{h1}=1.693\left(2\right), {\eta }_{\parallel }=-0.391\left(4\right)$, and ${\eta }_{\perp }=-0.179\left(5\right)$; in the extraordinary-log phase, the surface correlation function $C_{\parallel }\left(r\right)$ decays logarithmically with decaying exponent $q=0.60\left(2\right)$, however, the correlation $C_{\perp }\left(r\right)$ still decays algebraically with critical exponent ${\eta }_{\perp }=-0.442\left(5\right)$. If the ferromagnetic next-nearest-neighboring surface interactions are added, we find two transition points, the first one is a special point between the ordinary phase and the extraordinary-log phase, the second one is a transition between the extraordinary-log phase and the $Z_6$ symmetry-breaking phase, with critical exponent $y_{\mathrm{s}}=0.41\left(2\right)$. The scaling behaviors of the second transition is very interesting, the surface spin-correlation function $C_{\parallel }\left(r\right)$, and the surface squared staggered magnetization at this point decays logarithmically with exponent $q=0.37\left(1\right)$; however, the surface structure factor with the smallest wave vector and the correlation function $C_{\perp }\left(r\right)$ satisfy power-law decaying, with critical exponents ${\eta }_{\parallel }=-0.69\left(1\right)$ and ${\eta }_{\perp }=-0.37\left(1\right)$, respectively.

中文翻译：

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反铁磁 Potts 模型的表面临界性

我们研究了简单立方晶格上的三态反铁磁 Potts 模型，关注表面临界行为。当调整表面的最近邻相互作用时，由于体积临界点的紧急 O(2) 对称性，我们获得了类似于 XY 模型的相图。对于普通的过渡，我们得到${\mathrm{是的}}_{H1}=0.780\left(3\right), {\eta }_{\parallel }=1.44\left(1\right)$， 和${\eta }_{\perp }=0.736\left(6\right)$; 对于特殊的过渡，我们得到${\mathrm{是的}}_s=0.59\left(1\right), {\mathrm{是的}}_{H1}=1.693\left(2\right), {\eta }_{\parallel }=-0.391\left(4\right)$， 和${\eta }_{\perp }=-0.179\left(5\right)$; 在非常对数阶段，表面相关函数$C_{\parallel }\left(r\right)$以衰减指数对数衰减$q=0.60\left(2\right)$，但是，相关性$C_{\perp }\left(r\right)$仍然以临界指数代数衰减${\eta }_{\perp }=-0.442\left(5\right)$. 如果加上铁磁次最近邻表面相互作用，我们会发现两个过渡点，第一个是普通相和非常对数相之间的特殊点，第二个是非常对数相和非常对数相之间的过渡点。这$Z_6$对称破缺阶段，具有临界指数${\mathrm{是的}}_{\mathrm{s}}=0.41\left(2\right)$. 第二个跃迁的缩放行为非常有趣，表面自旋相关函数$C_{\parallel }\left(r\right)$，并且此时的表面平方交错磁化强度随指数对数衰减$q=0.37\left(1\right)$; 然而，具有最小波矢量的表面结构因子和相关函数$C_{\perp }\left(r\right)$满足幂律衰减，具有临界指数${\eta }_{\parallel }=-0.69\left(1\right)$和${\eta }_{\perp }=-0.37\left(1\right)$， 分别。