MonteCarlo方法在单极标度维数中的应用
Monopole scaling dimension using Monte Carlo
摘要：
通过对自由能的有限尺寸标度分析，提出了一种可行的确定通量$Q$阿贝尔磁单极标度尺寸$Δ_Q$的Monte Carlo方法.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$Δ_1= 0.13(2)$，$Δ_2=0.29(1)$和$Δ_3=0.47(2)$，我们发现它们正比于正方形环面上单极子的有限尺寸临界谱.
英文摘要：
We present a viable Monte Carlo determination of the scaling dimensions $Δ_Q$ 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 $Δ_1= 0.13(2)$, $Δ_2=0.29(1)$ and $Δ_3=0.47(2)$, which we find to be proportional to the finite-size critical spectrum of monopoles on square torus.
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