库仑抑制SU中库仑相的直接证据（2）格点规范理论
Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory
摘要：
进一步证明了在SU（2）格点规范理论中弱耦合时存在非限制相。利用标准威尔逊作用量的蒙特卡罗模拟，规范不变的SO（3）-Z 2单极子，这是强耦合的晶格伪像，已经看到经历了一个渗流过渡，正是在相变之前看到的库仑规范方法，与一个无限的晶格临界点附近$β= 3.2$。在强耦合（$β= 0$）极限下，对Z ~ 2涡旋和磁单极以及SO（3）-Z ~ 2磁单极的理论进行了数值模拟，直到$60^4$。在这里，正如威尔逊作用量理论的高$β$阶段一样，有限尺寸标度表明它自发地破坏了库仑规范固定后留下的剩余对称性。这种对称破缺排除了势的线性项。在任何$β$处，该限制似乎阻止了向限制相的转变。直接测量的瞬时库仑电位显示库仑形式与适度运行耦合可能接近红外固定点的$α\sim 1.4$。库仑势测量到50个晶格间距和2 fm。一个短距离拟合的2圈微扰势被用来设置的规模。在如此长的距离上的高精度是通过使用开边界条件而成为可能的，以前发现开边界条件显著地减少了库仑规固定过程的随机误差和系统误差。库仑势与用周期晶格上的威尔逊环测量的规范不变夸克间势一致，只要后者可以用类似的统计数据实际测量。
英文摘要：
Further evidence is presented for the existence of a non-confining phase at weak coupling in SU(2) lattice gauge theory. Using Monte Carlo simulations with the standard Wilson action, gauge-invariant SO(3)-Z2 monopoles, which are strong-coupling lattice artifacts, have been seen to undergo a percolation transition exactly at the phase transition previously seen using Coulomb-gauge methods, with an infinite lattice critical point near $β= 3.2$. The theory with both Z2 vortices and monopoles and SO(3)-Z2 monopoles eliminated is simulated in the strong coupling ($β= 0$) limit on lattices up to $60^4$. Here, as in the high-$β$ phase of the Wilson action theory, finite size scaling shows it spontaneously breaks the remnant symmetry left over after Coulomb gauge fixing. Such a symmetry breaking precludes the potential from having a linear term. The monopole restriction appears to prevent the transition to a confining phase at any $β$. Direct measurement of the instantaneous Coulomb potential shows a Coulombic form with moderately running coupling possibly approaching an infrared fixed point of $α\sim 1.4$. The Coulomb potential is measured to 50 lattice spacings and 2 fm. A short-distance fit to the 2-loop perturbative potential is used to set the scale. High precision at such long distances is made possible through the use of open boundary conditions, which was previously found to cut random and systematic errors of the Coulomb gauge fixing procedure dramatically. The Coulomb potential agrees with the gauge-invariant interquark potential measured with smeared Wilson loops on periodic lattices as far as the latter can be practically measured with similar statistics data.
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