论文标题
抗铁磁POTTS模型的表面临界
Surface criticality of antiferromagnetic Potts model
论文作者
论文摘要
我们研究了简单的立方晶格上的三态抗磁性POTTS模型，以关注表面关键行为。当对表面的最近相邻相互作用进行调整时，我们获得了类似于XY模型的相图，这是由于块状临界点的出现O（2）对称性。对于普通过渡，我们得到$ y_ {h1} = 0.780（3）$，$η_\ Parallel = 1.44（1）$，$η_\ perp = 0.736（6）$;对于特殊过渡，我们得到$ y_s = 0.59（1）$，$ y_ {h1} = 1.693（2）$，$η_\ Parallel = -0.391（4）$和$η_\ perp = -0.179（5）$;在非同寻常的阶段，表面相关函数$ c_ \ parallel（r）$衰减对数，而衰减的指数$ q = 0.60（2）$，但是，相关性$ c_ \ perp（r）$仍然衰减代数，而crigital $ perpents $ n_ \ perp = perp = -0.442 $。如果添加了铁电磁的下一个邻近的表面相互作用，我们发现两个过渡点，第一个是普通阶段和非凡阶段之间的特殊点，第二个是特殊的阶段，第二个是非凡的log阶段和$ z_6 $对称性阶段之间的过渡，其中关键指数$ y _ _ _ _ _ _ _ _ _ _ {\ rm s} = 0.41 = 0.41 = 0.41（2）$。第二个过渡的缩放行为非常有趣，表面旋转相关函数$ c_ \ parallel（r）$和表面平方的交错磁化强度在这一点上衰减，而指数$ q = 0.37（1）$;但是，具有最小波矢量和相关函数的表面结构因子$ c_ \ perp（r）$满足幂律衰减，其中关键指数$η_\ Parallel = -0.69（1）$和$η_\ perp = -0.37（1）$。
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 $y_{h1}=0.780(3)$, $η_\parallel=1.44(1)$, and $η_\perp=0.736(6)$; for the special transition, we get $y_s=0.59(1)$, $y_{h1}=1.693(2)$, $η_\parallel=-0.391(4)$, and $η_\perp=-0.179(5)$; in the extraordinary-log phase, the surface correlation function $C_\parallel(r)$ decays logarithmically, with decaying exponent $q=0.60(2)$, however, the correlation $C_\perp(r)$ still decays algebraically, with critical exponent $η_\perp=-0.442(5)$. 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 $y_{\rm s}=0.41(2)$. The scaling behaviors of the second transition is very interesting, the surface spin correlation function $C_\parallel(r)$ and the surface squared staggered magnetization at this point decays logarithmically, with exponent $q=0.37(1)$; however, the surface structure factor with the smallest wave vector and the correlation function $C_\perp(r)$ satisfy power-law decaying, with critical exponents $η_\parallel=-0.69(1)$ and $η_\perp=-0.37(1)$, respectively.
