标题： 共形不变性约束在$O(N)$模型中：非微扰重整化群中的初步研究 显示英文标题

标题： Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group

摘要： 许多临界现象在大尺度下的行为预计将是全共形群的不变量，而不仅仅是等距变换和标度变换。 当研究临界现象时，通常需要近似处理，非微扰框架或者函数重正化群方法也不例外。 由于在过去几十年中，在多个系统上表现出色，导数展开是该框架中最流行的近似方案之一。 然而，它有一个缺点，即在有限阶次上破坏了共形对称性。 这种破坏在展开的主阶（称为LPA近似）中未被观察到，只有在至少考虑导数展开的下一阶（$\mathcal{O}(\partial^2)$），并且包括复合算符时才会出现。 在这项工作中，我们使用导数展开至$\mathcal{O}(\partial^2)$阶次，研究了$O(N)$模型中由共形对称性引起的约束条件。 我们探索了$N$的各种值，并最小化了共形对称性的破坏，以固定近似过程中的非物理参数。 我们将我们对临界指数的预测与更常用的最小敏感性原理得到的结果进行了比较。 显示英文摘要

摘要： 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 last 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 LPA approximation, and only appears once one considers, at least, the next-to-leading order of the derivative expansion ($\mathcal{O}(\partial^2)$) 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 $\mathcal{O}(\partial^2)$. We explore various values of $N$ and minimize the breaking of conformal symmetry to fix the non-physical 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.