AI 中文总结
本文针对三维伊辛普适类，研究导数展开4阶截断下的共形Ward恒等式，发现调节函数对临界指数影响小，共形破缺随导数阶数增加而降低，为导数展开近似的收敛性提供新证据。
AI 中文摘要
共形不变性被认为是许多系统在临界区域的涌现性质，但近似方案通常会破坏该性质，导数展开（functional renormalization group框架中广泛使用的近似方案）尤其如此。本文研究三维伊辛普适类中共形不变性相关的Ward恒等式，采用导数展开的4阶（次次领头阶）截断，包含Z₂不变复合算子。结果表明，使共形不变性产生微小破缺的调节函数，其选择对普适临界指数的敏感性也很小；还显示在共形约束满足度最佳的调节参数值附近，共形不变性的破缺程度随导数展开阶数增加而降低，为该近似方案的收敛性提供了新的佐证。
英文摘要
Conformal invariance is expected to be an emergent property of many systems in their critical regime. However, approximation schemes generically spoil this property. This is in particular the case of the derivative expansion, a widely used approximation scheme in the framework of the functional renormalization group. In this article, we consider Ward identities associated with conformal invariance in the 3-d Ising universality class with truncations at order 4 (next-to-next-to-leading order) in the derivative expansion, with $Z_2$ invariant composite operators. Our results confirm that the regulating functions which yield a small breaking of conformal invariance also present a small sensitivity of the universal critical exponents with the choice of this regulating function. We also show that, in the vicinity of regulator-parameter values for which the conformal constraints are best satisfied, the breaking of conformal invariance reduces as the order of the derivative expansion is increased, providing a new indication of the convergence of this approximation scheme.
Comments13 pages, 6 figures
