论文标题
Bardeen-Moshe-Bander现象的有限$ n $起源及其扩展为$ n = \ indull固定点
The finite $N$ origin of the Bardeen-Moshe-Bander phenomenon and its extension at $N=\infty$ by singular fixed points
论文作者
论文摘要
我们研究了$ o（n）$型号的尺寸三（3 $ d $），该型号在大而无限的$ n $上，表明在$ n = \ infty $的固定点线 - Bardeen-Moshe-Bander（BMB）系列 - 在有限$ n $中具有有趣的起源。允许我们找到BMB线的大$ n $限制必须在$（d，n）$ - 平面：$ d = 3-α/n $的特定轨迹上进行，而不是在固定尺寸$ d = 3 $上。我们的研究还表明，已知的BMB线只是固定点的真实线的一半，下半部分是由单数固定点制成的。这些单数固定点的电位显示了该场的有限值及其有限的$ n $对应物的尖端。
We study the $O(N)$ model in dimension three (3$d$) at large and infinite $N$ and show that the line of fixed points found at $N=\infty$ --the Bardeen-Moshe-Bander (BMB) line-- has an intriguing origin at finite $N$. The large $N$ limit that allows us to find the BMB line must be taken on particular trajectories in the $(d,N)$-plane: $d=3-α/N$ and not at fixed dimension $d=3$. Our study also reveals that the known BMB line is only half of the true line of fixed points, the second half being made of singular fixed points. The potentials of these singular fixed points show a cusp for a finite value of the field and their finite $N$ counterparts a boundary layer.
