标题： 三维$O(N)$模型极端对数边界相中的普遍有限尺寸标度 显示英文标题

标题： Universal finite-size scaling in the extraordinary-log boundary phase of three-dimensional $O(N)$ model

摘要： 最近在边界临界现象方面的进展导致在三维$O(N)$模型中发现了一个新的表面普适类。 新发现的“非凡对数”相可以在二维表面上实现，对于$N< N_c$，具有$N_c>3$，也可以在嵌入三维系统中的平面缺陷上实现，对于任何$N$。 “非凡对数”相的一个关键特征是标准有限尺寸标度的对数违反。 在本工作中，我们通过改进的格点模型的蒙特卡洛模拟来研究“非凡对数”普适类中的有限尺寸标度。 我们使用开放边界条件模拟该模型，在$N=2,3$的表面上实现“非凡对数”相，以及在完全周期性边界条件和存在平面缺陷的情况下，对于$N=2,3,4$进行模拟。 与理论预测一致，此处研究的重整化群不变可观测量表现出与系统大小的对数依赖关系。 我们数值上不仅获得了控制这些对数违背的$\beta$函数中的主要项，还获得了次主要项，该次主要项控制着边界相图随$N$的演化。 显示英文摘要

摘要： Recent advances in boundary critical phenomena have led to the discovery of a new surface universality class in the three-dimensional $O(N)$ model. The newly found ``extraordinary-log" phase can be realized on a two-dimensional surface for $N< N_c$, with $N_c>3$, and on a plane defect embedded into a three-dimensional system, for any $N$. One of the key features of the extraordinary-log phase is the presence of logarithmic violations of standard finite-size scaling. In this work we study finite-size scaling in the extraordinary-log universality class by means of Monte Carlo simulations of an improved lattice model. We simulate the model with open boundary conditions, realizing the extraordinary-log phase on the surface for $N=2,3$, as well as with fully periodic boundary conditions and in the presence of a plane defect for $N=2,3,4$. In line with theory predictions, renormalization-group invariant observables studied here exhibit a logarithmic dependence on the size of the system. We numerically access not only the leading term in the $\beta$-function governing these logarithmic violations, but also the subleading term, which controls the evolution of the boundary phase diagram as a function of $N$.