Conformal invariance in the nonperturbative renormalization group: A rationale for choosing the regulator.,Physical Review E

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Conformal invariance in the nonperturbative renormalization group: A rationale for choosing the regulator.
Physical Review E ( IF 2.2 ) Pub Date : 2020-06-29 , DOI: 10.1103/physreve.101.062146
Ivan Balog ₁ , Gonzalo De Polsi ₂ , Matthieu Tissier ₃ , Nicolás Wschebor ₄

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Field-theoretical calculations performed in an approximation scheme often present a spurious dependence of physical quantities on some unphysical parameters associated with the details of the calculation setup (such as the renormalization scheme or, in perturbation theory, the resummation procedure). In the present article, we propose to reduce this dependence by invoking conformal invariance. Using as a benchmark the three-dimensional Ising model, we show that, within the derivative expansion at order 4, performed in the nonperturbative renormalization group formalism, the identity associated with this symmetry is not exactly satisfied. The calculations which best satisfy this identity are shown to yield critical exponents which coincide to a high accuracy with those obtained by the conformal bootstrap. Additionally, this work gives a strong justification to the success of a widely used criterion for fixing the appropriate renormalization scheme, namely the principle of minimal sensitivity.

中文翻译：

非摄动重归一化组的共形不变性：选择调节器的基本原理。

在逼近方案中执行的场理论计算通常表示物理量对某些与计算设置的细节相关联的非物理参数的虚假依赖（例如，重新归一化方案，或者在扰动理论中，是恢复过程）。在本文中，我们建议通过调用共形不变性来减少这种依赖性。使用三维Ising模型作为基准，我们表明，在非扰动重正态化组形式主义中进行的4阶导数展开内，与该对称性相关的身份不能完全满足。结果表明，最能满足该身份的计算得出的临界指数与保形自举所获得的临界指数高度吻合。另外，

更新日期：2020-06-29

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