Conformal invariance constraints in the O(N) models: A study within the nonperturbative renormalization group.

IF 2.2 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS
Santiago Cabrera, Gonzalo De Polsi, Nicolás Wschebor
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引用次数: 0

Abstract

The behavior of many critical phenomena at large distances is expected to be invariant under the full conformal group, rather than only isometries and scale transformations. When studying critical phenomena, approximations are often required, and the framework of the nonperturbative, or functional, renormalization group is no exception. The derivative expansion is one of the most popular approximation schemes within this framework, due to its great performance on multiple systems, as evidenced in the past few decades. Nevertheless, it has the downside of breaking conformal symmetry at a finite order. This breaking is not observed at the leading order of the expansion, denoted the local potential approximation, and it only appears once one considers, at least, the next-to-leading order of the derivative expansion [O(∂^{2})] when including composite operators. In this work, we study the constraints arising from conformal symmetry for the O(N) models using the derivative expansion at order O(∂^{2}). We explore various values of N and minimize the breaking of conformal symmetry to fix the nonphysical parameters of the approximation procedure. We compare our prediction for the critical exponents with those coming from a more usual procedure, known as the principle of minimal sensitivity.

O(N)模型的保形不变性约束:非微扰重整化群内的研究。
许多临界现象在大距离上的行为在全共形群下是不变的,而不仅仅是等距和尺度变换。在研究临界现象时,通常需要近似,非微扰或泛函重整化群的框架也不例外。在过去的几十年里,由于导数展开在多个系统上的优异性能,它是该框架中最受欢迎的近似方案之一。然而,它有在有限阶上破坏共形对称的缺点。在展开的前导阶上没有观察到这种破坏,表示局部势近似,并且只有当人们考虑到包含复合算子的导数展开[O(∂^{2})]的次前导阶时,它才会出现。在这项工作中,我们使用O(∂^{2})阶的导数展开研究O(N)模型的共形对称性产生的约束。我们探索不同的N值,并最小化保形对称性的破坏,以固定近似过程的非物理参数。我们将我们对临界指数的预测与更常用的程序(称为最小灵敏度原理)的预测进行比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Physical Review E
Physical Review E PHYSICS, FLUIDS & PLASMASPHYSICS, MATHEMAT-PHYSICS, MATHEMATICAL
CiteScore
4.50
自引率
16.70%
发文量
2110
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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