发表机构
HUN-REN–ELTE Theoretical Physics Research Group; Theory Department, HUN-REN Wigner RCP（匈牙利研究与创新网络-罗兰大学理论物理研究组; 匈牙利研究与创新网络维格纳研究中心理论部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用 Kurganov--Tadmor 和网格方法求解两味夸克-介子模型的泛函重整化群流，验证了 LPA$'$ 截断下网格法的精度，并发现低温一阶相边界回弯现象在 LPA$'$ 中依然存在。
AI 中文摘要
我们使用 Kurganov--Tadmor 中心格式和标准网格方法，在局域势近似（LPA）以及包含π介子、σ介子和夸克场传播波函数重整化因子的 LPA$'$ 截断下，利用 Litim 调节器求解了有限温度和有限夸克化学势下两味夸克-介子模型的泛函重整化群流。我们将 Kurganov--Tadmor 格式作为高分辨率基准，一直计算到极低温度，此时费米面在势场的场导数中产生最尖锐的前沿。我们发现，在足够精细的分辨率下，网格方法在两种截断中给出的结果几乎与基准完全一致。我们讨论了波函数重整化因子给模型参数化以及有限密度下流动带来的困难，这些困难与展开点的选择有关。与某些预期相反，从 LPA 中已知的低温下一阶相边界特有的回弯现象，在我们实现的 LPA$'$ 截断中仍然存在，无论是采用固定展开点还是流动展开点。
英文摘要
We solve the functional renormalization group flow of the two-flavor quark-meson model at finite temperature and quark chemical potential with Litim's regulator, using the Kurganov--Tadmor central scheme and the standard grid method, both in the local potential approximation (LPA) and in an LPA$'$ truncation with running wave function renormalization factors for the pion, sigma, and quark fields. Using the Kurganov--Tadmor scheme as a high-resolution benchmark down to very low temperatures, where the Fermi surface produces the sharpest fronts in the field derivative of the potential, we find that, with sufficiently fine resolution, the grid method gives virtually identical results in both truncations. We discuss the difficulties that the wave function renormalization factors bring into the parametrization of the model and into the flow at finite density, related to the choice of the expansion point. Contrary to some expectations, the peculiar backbending of the first-order phase boundary at low temperature, known from LPA, persists in our implementation of the LPA$'$ truncation, both with a fixed and with a running expansion point.
Comments37 pages, 6 figures, 1 table
