标题： 二维Potts模型中的累积量及其比值的排序：QCD的经验教训？ 显示英文标题

标题： Cumulants and ordering of their ratios in 2D Potts models: Lessons for QCD?

摘要： 理论考虑表明，在净重子化学势较小的情况下，从低温介子相到高温夸克胶子等离子体相的转变附近，净重子数涨落比的顺序排列出现在QCD相图中的 $\mu_B$ 区域。 这个顺序层次结构是 $\frac{\chi_6}{\chi_2} < \frac{\chi_5}{\chi_1} < \frac{\chi_4}{\chi_2} < \frac{\chi_3}{\chi_1}$，其中 $\chi_n$ 是净重子数涨落的 $n^\mathrm{th}$ 阶累积量。 STAR 实验在一系列碰撞能量范围内观察到了净质子数（净重子数的代理）累积量比的这种层次结构。 这些不等式可以通过在模型中取相应的阶参数作为重子密度的类比来在自旋模型中进行检验。 我们采用了两种不同的模型：二维两态和三态Potts模型，它们分别在各自的临界温度处经历从有序相到无序相的转变。 使用Wolff算法在不同大小的正方形网格上进行了模拟。 在这两个模型中，在接近各自临界温度的温度范围内得到了总磁化强度的累积量，直到第六阶。 随着晶格尺寸的增加，高阶累积量的峰值（谷值）的高度似乎随着累积量阶数的增加而增加。 除了三态Potts模型临界温度以上的一个狭窄范围外，在模拟的温度范围内，完全满足不等式或其完全反向的情况并未出现。 显示英文摘要

摘要： Theoretical considerations suggest an ordering of the ratios of net-baryon number fluctuations in the vicinity of the transition from the low-temperature hadronic phase to the high temperature quark-gluon plasma phase at small values of the baryon chemical potential, $\mu_B$, in the QCD phase diagram. The ordering hierarchy is $\frac{\chi_6}{\chi_2} < \frac{\chi_5}{\chi_1} < \frac{\chi_4}{\chi_2} < \frac{\chi_3}{\chi_1}$, where $\chi_n$ is the $n^\mathrm{th}$ order cumulant of net-baryon number fluctuation. The STAR experiment observed this hierarchy in the ordering of cumulant ratios of net-proton number (a proxy of net-baryon number) for a range of colliding energies. These inequalities can be tested in spin models by taking the corresponding order parameters in the model as an analog of baryon density. We employed two different models: the two-state and three-state Potts models in two dimensions, which undergo a transition from an ordered phase to a disordered phase at their respective critical temperature. Simulations were performed on square lattices of different sizes using the Wolff algorithm. The cumulants of total magnetization are obtained up to the sixth order in both of these models in a temperature range near their corresponding critical temperatures. With increasing lattice size, height (trough) of the peaks (dips) of the higher-order cumulants appears to increase with the increase in the order of the cumulants. Except in a narrow range above the critical temperature of the three-state Potts model, the complete inequality or its complete reverse is not satisfied in the temperature ranges simulated.