绘制二维和三维伊辛普适类的标度区域
Charting the scaling region of the Ising universality class in two and three dimensions
摘要：
我们研究的行为的磁化率和相关长度的普遍组合在伊辛模型在二维和三维，在存在磁和热扰动，在临界点附近。在三维中，我们使用状态方程的参数化表示来解决这个问题。在二维中，我们利用模型沿热轴和磁轴的精确可积性。我们的结果可以作为一种“参考系“来绘制模型的临界区域。虽然我们的结果可以适用于任何可能实现的伊辛普适性类的原则，我们特别地址，作为具体的例子，伊辛行为在有限温度QCD相关的各种方式的解除禁闭过渡的三个实例。特别地，在最后一个例子中，我们研究了有限密度、有限温度的QCD相图中的临界终点。在这个有限密度框架中，由于众所周知的符号问题，蒙特卡洛模拟是不可能的，因此直接比较实验结果与QFT/Statmech预测，如我们在本文中讨论的一个可能是重要的。此外，在这个例子中，它是特别困难的解开“类磁”从“类热”的可观的，因此，不需要一个精确的识别的磁轴和热轴，像我们在本文中解决的通用量，可以是特别有用的。
英文摘要：
We study the behaviour of a universal combination of susceptibility and correlation length in the Ising model in two and three dimensions, in presence of both magnetic and thermal perturbations, in the neighbourhood of the critical point. In three dimensions we address the problem using a parametric representation of the equation of state. In two dimensions we make use of the exact integrability of the model along the thermal and the magnetic axes. Our results can be used as a sort of "reference frame" to chart the critical region of the model. While our results can be applied in principle to any possible realization of the Ising universality class, we address in particular, as specific examples, three instances of Ising behaviour in finite temperature QCD related in various ways to the deconfinement transition. In particular, in the last of these examples, we study the critical ending point in the finite density, finite temperature phase diagram of QCD. In this finite density framework, due to well know sign problem, Montecarlo simulations are not possible and thus a direct comparison of experimental results with QFT/Statmech predictions like the one we discuss in this paper may be important. Moreover in this example it is particularly difficult to disentangle "magnetic-like" from "thermal-like" observables and thus universal quantities which do not need a precise identification of the magnetic and thermal axes, like the one we address in this paper, can be particularly useful.
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