Monopole scaling dimension using Monte-Carlo simulation
Monopole scaling dimension using Monte-Carlo simulation
复制标题
使用蒙特卡罗模拟的单极子缩放尺寸
DOI：
10.1103/physrevd.98.074513
复制
发表时间：
2018
影响因子：
5
通讯作者：
Nikhil Karthik
中科院分区：
文献类型：
--
作者：
Nikhil Karthik
我们提出了一个可行的Monte Carlo确定的标度尺寸$\Delta_Q$的通量$Q$阿贝尔单极通过有限尺寸标度分析的自由能引入的背景场的经典狄拉克夸克-反夸克对在临界点的三维晶格理论。我们在自由费米子理论中验证了该方法的有效性，并通过验证反XY不动点处的电荷标度维数与反XY不动点处的电荷标度维数之间的粒子涡旋对偶性来验证该方法的有效性.在O（2）$ Wilson-Fisher不动点处，我们确定了临界指数$\Delta_1 = 0.13（2）$，$\Delta_2 =0.29（1）$和$\Delta_3 =0.47（2）$，我们发现它们与正方形环面上单极子的有限尺寸临界谱成正比.
We present a viable Monte Carlo determination of the scaling dimensions $\Delta_Q$ of flux $Q$ Abelian monopoles through finite-size scaling analysis of the free energy to introduce the background field of classical Dirac monopole-antimonopole pair at critical points of three-dimensional lattice theories. We validate the method in free fermion theory, and by verifying the particle-vortex duality between the monopole scaling dimension at the inverse-XY fixed point and the charge scaling dimension at the XY fixed point. At the $O(2)$ Wilson-Fisher fixed point, we determine the critical exponents $\Delta_1= 0.13(2)$, $\Delta_2=0.29(1)$ and $\Delta_3=0.47(2)$, which we find to be proportional to the finite-size critical spectrum of monopoles on square torus.