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Charting the scaling region of the Ising universality class in two and three dimensions
Physical Review D ( IF 5 ) Pub Date : 2020-07-10 , DOI: 10.1103/physrevd.102.014505
Michele Caselle , Marianna Sorba

We study the behavior 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 neighborhood 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 behavior 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 the well-known sign problem, Monte Carlo simulations are not possible and thus a direct comparison of experimental results with quantum field theory statistical mechanics 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 an explicit charting of the neighborhood of the critical point can be particularly useful.

中文翻译:

在二维和三个维度上绘制 Ising 普适性类的缩放区域

我们在临界点附近,在存在磁扰动和热扰动的情况下,在二维和三个维度上研究 Ising 模型中磁化率和相关长度的通用组合的行为。在三个维度中,我们使用状态方程的参数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。虽然我们的结果原则上可以应用于 Ising 普遍性类的任何可能的实现,但我们特别强调,作为具体例子,有限温度 QCD 中 Ising 行为的三个实例以各种方式与解除限制转变相关。特别是,在最后一个例子中,我们研究了 QCD 有限密度、有限温度相图中的临界点。在这个有限密度框架中,由于众所周知的符号问题,蒙特卡罗模拟是不可能的,因此将实验结果与我们在本文中讨论的量子场论统计力学预测进行直接比较可能很重要。此外,在这个例子中,将“类磁”与“类热”可观测数据区分开来特别困难,因此临界点附近的显式图表可能特别有用。蒙特卡罗模拟是不可能的,因此将实验结果与我们在本文中讨论的量子场论统计力学预测进行直接比较可能很重要。此外,在这个例子中,将“类磁”与“类热”可观测数据区分开来特别困难,因此临界点附近的显式图表可能特别有用。蒙特卡罗模拟是不可能的,因此将实验结果与我们在本文中讨论的量子场论统计力学预测进行直接比较可能很重要。此外,在这个例子中,将“类磁”与“类热”可观测数据区分开来特别困难,因此临界点附近的显式图表可能特别有用。
更新日期:2020-07-10
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