受最近对六方晶系铁氧体的实验观察[Phys. Rev. 96，020407（2017）]的启发，我们重新审视了接近晶格逾渗阈值的稀释磁体的相图。我们进行大规模的Monte Carlo模拟XY和海森堡模型上的简单立方晶格和晶格代表的六方晶系铁氧体的晶体结构。在接近渗流阈值$p_c$时，我们发现磁有序温度$T_c$与稀释度$p$的关系符合幂律$T_c \sim |p-p_c|^ϕ$和指数$ϕ=1.09$，与经典渗流理论一致.然而，这个渐近临界区域非常窄，$|p-p_c| \lesssim 0.04$。在它之外，相边界的形状在很宽的稀释范围内可以用指数略低于1的非普适幂律很好地描述。尽管如此，渗流方案并不再现PbFe $_{12-x}$ Ga $_x$ O $_{19}$中实验观察到的关系$T_c \sim (x_c -x)^{2/3}$。我们讨论了我们的研究结果的一般性，以及对物理学的影响稀释六角铁氧体。
英文摘要：
Motivated by recent experimental observations [Phys. Rev. 96, 020407 (2017)] on hexagonal ferrites, we revisit the phase diagrams of diluted magnets close to the lattice percolation threshold. We perform large-scale Monte Carlo simulations of XY and Heisenberg models on both simple cubic lattices and lattices representing the crystal structure of the hexagonal ferrites. Close to the percolation threshold $p_c$, we find that the magnetic ordering temperature $T_c$ depends on the dilution $p$ via the power law $T_c \sim |p-p_c|^ϕ$ with exponent $ϕ=1.09$, in agreement with classical percolation theory. However, this asymptotic critical region is very narrow, $|p-p_c| \lesssim 0.04$. Outside of it, the shape of the phase boundary is well described, over a wide range of dilutions, by a nonuniversal power law with an exponent somewhat below unity. Nonetheless, the percolation scenario does not reproduce the experimentally observed relation $T_c \sim (x_c -x)^{2/3}$ in PbFe$_{12-x}$Ga$_x$O$_{19}$. We discuss the generality of our findings as well as implications for the physics of diluted hexagonal ferrites.
Griffiths phase in clique percolation in random geometric graphs
Laboratory of Complex Networks, Center for Neurophysics and Neuromorphic Technologies（复杂网络实验室，神经物理与神经形态技术中心）；Moscow Institute for Physics and Technology, Phystech School of Applied Mathematics and Computer Science（莫斯科物理技术学院，应用数学与计算机科学普希钦学院）；Department of Applied Mathematics, MIEM, National Research University Higher School of Economics（高等经济大学信息工程与管理学院应用数学系）；Kharkevich Institute for Information Transmission Problems RAS（俄罗斯科学院哈拉维奇信息传输问题研究所）
