关键终点位置的可靠下限
Towards a reliable lower bound on the location of the critical endpoint
摘要：
利用2-stout改进的有根交错费米子的数值模拟，首次在格点量子色动力学中直接确定了压力在复化学势$μ_B$平面上的主导奇点位置.这提供了压力的泰勒展开的收敛半径的直接确定，而不依赖于展开的有限阶截断。在不改变观测量的连续极限的前提下，通过重新定义费米子行列式，使其成为任意有限格点上逸度的多项式，解决了具有交错费米子根的QCD巨正则配分函数在复$μ_B$平面上的解析性问题.通过在一个单一的粗晶格间距进行有限体积标度的研究，我们表明，极限奇点是不是在真正的线上的热力学极限，从而表明泰勒展开的收敛半径给出了一个可能的相变的位置上的下限。在零化学势的交叉温度附近，收敛半径为$μ_B/T \approx 2$，且与温度无关。
英文摘要：
We perform the first direct determination of the position of the leading singularity of the pressure in the complex chemical potential $μ_B$ plane in lattice QCD using numerical simulations with 2-stout improved rooted staggered fermions. This provides a direct determination of the radius of convergence of the Taylor expansion of the pressure that does not rely on a finite-order truncation of the expansion. The analyticity issues in the complex $μ_B$ plane of the grand canonical partition function of QCD with rooted staggered fermions are solved with a careful redefinition of the fermion determinant that makes it a polynomial in the fugacity on any finite lattice, without changing the continuum limit of the observables. By performing a finite volume scaling study at a single coarse lattice spacing, we show that the limiting singularity is not on the real line in the thermodynamic limit, thus showing that the radius of convergence of the Taylor expansion gives a lower bound on the location of a possible phase transition. In the vicinity of the crossover temperature at zero chemical potential, the radius of convergence turns out to be $μ_B/T \approx 2$ and roughly temperature independent.
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