Surface criticality of antiferromagnetic Potts model

Abstract

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 $y_{h1}=0.780(3)$, ${\eta }_{\parallel }=1.44(1)$, and ${\eta }_{\perp }=0.736(6)$; for the special transition, we get $y_s=0.59(1)$, $y_{h1}=1.693(2)$, ${\eta }_{\parallel }=-0.391(4)$, and ${\eta }_{\perp }=-0.179(5)$; 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 ${\eta }_{\perp }=-0.442(5)$. 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 $y_{\mathrm{s}}=0.41(2)$. 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 ${\eta }_{\parallel }=-0.69(1)$ and ${\eta }_{\perp }=-0.37(1)$, respectively.

8 pages,8 figures

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Cited by in corpus (14)

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• Quantum extraordinary-log universality of boundary critical behavior
• Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge
• Sublattice extraordinary-log phase and new special point of the antiferromagnetic Potts model
• Comprehensive studies on the universality of BKT transitions -- Machine-learning study, Monte Carlo simulation, and Level-spectroscopy method
• Emergent topological ordered phase for the Ising-XY Model revealed by cluster-updating Monte-Carlo method
• Boundary criticality for the Gross-Neveu-Yukawa models
• Boundary phase transitions of two-dimensional quantum critical XXZ model
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Crossover in the Ordered Phase in the Non-Mermin-Wagner-Hohenberg Regime of Spin Models with Long-Range Coupling
• Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter