Scaling solutions in the derivative expansion

N. Defenu; A. Codello

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Scaling solutions in the derivative expansion

机译：导数扩展中的缩放解决方案

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Scalar field theories with Z 2 symmetry are the traditional playground of critical phenomena. In this work, these models are studied using functional renormalization group (FRG) equations at order ? 2 of the derivative expansion and, differently from previous approaches, the spike plot technique is employed to find the relative scaling solutions in two and three dimensions. The anomalous dimension of the first few universality classes in d = 2 is given, and the phase structure predicted by conformal field theory is recovered (without the imposition of conformal invariance), while in d = 3 a refined view of the standard Wilson-Fisher fixed point is found. Our study enlightens the strength of shooting techniques in studying FRG equations, suggesting them as candidates to investigate strongly nonperturbative theories even in more complex cases.

机译：具有Z 2对称性的标量场理论是临界现象的传统领域。在这项工作中，这些模型使用功能重整化组（FRG）方程进行了研究。与微分展开的图2相比，与以前的方法不同，采用了尖峰图技术来找到二维和三维的相对缩放解。给出了d = 2中前几个通用性类别的反常维数，并且恢复了由共形场理论预测的相结构（没有施加共形不变性），而在d = 3中，对标准Wilson-Fisher进行了改进找到固定点。我们的研究启发了射击技术在研究FRG方程中的优势，建议他们甚至在更复杂的情况下也可以作为研究非扰动性强的理论的候选人。

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《Physical review, D》 |2018年第1期|共13页
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N. Defenu; A. Codello;
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1. Scaling solutions in the derivative expansion [J] . N. Defenu, A. Codello Physical review, D . 2018,第1aPta2期

机译：衍生扩展中的缩放解决方案
2. THE KBM DERIVATIVE EXPANSION METHOD IS EQUIVALENT TO THE MULTIPLE-TIME-SCALES METHOD [J] . Hassan A. Journal of Sound and Vibration . 1997,第4期

机译：KBM导数展开法等效于多时间尺度方法
3. Spherical Harmonics Expansion of Fundamental Solutions and Their Derivatives for Homogeneous Elliptic Operators [J] . Vincenzo Gulizzi, Ivano Benedetti, Alberto Milazzo Journal of Multiscale Modelling . 2017,第3a4期

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4. Large-Scale MDO of a Small Satellite using a Novel Framework for the Solution of Coupled Systems and their Derivatives [C] . John T. Hwang, Dae Young Lee, James W. Cutler, AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference . 2013

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7. Scaling solutions in the derivative expansion [O] . Defenu, N., Codello, A. 2017

机译：在衍生扩展中扩展解决方案

Scaling solutions in the derivative expansion

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