论文标题

在两个维度和三个维度上绘制Ising通用类别的缩放区域

Charting the scaling region of the Ising universality class in two and three dimensions

论文作者

Caselle, Michele, Sorba, Marianna

论文摘要

我们研究了临界点附近的磁性和热扰动,在磁和热扰动的情况下,在两个维度和三个维度中,易感性和相关长度的普遍组合的行为。在三个维度中,我们使用状态方程的参数表示解决了问题。在二维中,我们利用沿热轴和磁轴的模型的确切整合性。我们的结果可以用作一种“参考框架”来绘制模型的关键区域。虽然我们的结果可以原则上应用于Ising通用类别类别的任何可能实现的可能实现,但我们特别是作为特定示例,在有限温度QCD中以各种方式与解解过渡相关的三个实例。特别是,在这些示例的最后一个示例中,我们研究了有限密度,有限温度相图的临界终点。在这个有限的密度框架中,由于符合符号问题,蒙特卡洛模拟是不可能的,因此可以直接比较实验结果与QFT/Statmech预测,例如我们在本文中讨论的QFT/Statmech预测可能很重要。此外,在此示例中,特别困难地将“磁性”从“热的”可观察物中解散,因此不需要精确识别磁性和热轴的通用量,例如我们在本文中所解决的轴,这是特别有用的。

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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