哥伦比亚图的连续极限和普适性
Continuum limit and universality of the Columbia plot
摘要：
在哥伦比亚图左下角的三种简并味QCD的热跃迁结果是令人困惑的。对于无质量的夸克，跃迁预计是一阶的，对于一定范围的夸克质量，跃迁将保持一阶，直到在临界夸克质量处转变为二阶。但在有限的晶格间距下，Wilson和交错费米子的临界夸克质量和由此产生的“π”质量不一致，并且至少对于交错费米子，临界夸克质量和由此产生的“π”质量随晶格间距的增加而急剧减小。为了澄清这一难题，消除潜在的系统效应的根源，我们研究了交错费米子的4味理论，在晶格上有4到10个时间片。我们的结果是定性类似的3味的情况下，所以生根不是一个问题。然而，戏剧性的截止效应是可见的，即使在我们最好的晶格上。普适性意味着威尔逊费米子的截止效应甚至更引人注目。为了在连续介质理论中获得一级热跃迁，需要极轻的夸克。
英文摘要：
Results on the thermal transition of QCD with 3 degenerate flavors, in the lower-left corner of the Columbia plot, are puzzling. The transition is expected to be first-order for massless quarks, and to remain so for a range of quark masses until it turns second-order at a critical quark mass. But this critical quark mass and resulting "pion" mass disagree violently between Wilson and staggered fermions at finite lattice spacing, and decrease sharply with the lattice spacing, for staggered fermions at least. To clarify this puzzle and eliminate potential systematic effects from rooting, we study the 4-flavor theory with staggered fermions, on lattices with 4 to 10 time-slices. Our results are qualitatively similar to the 3-flavor case, so that rooting is not an issue. However, dramatic cutoff effects are visible, even on our finest lattices. Universality implies that cutoff effects for Wilson fermions are even more dramatic. In order to obtain a first-order thermal transition in the continuum theory, extremely light quarks are needed.
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