FRG中的多参数优化探索
Exploring multi-parameter optimization in FRG
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中文总结 AI 辅助
本文在FRG框架下提出多参数调节器优化方法，通过最小敏感性原理在四阶导数展开中改善三维Ising临界指数预测，并发现紧致调节器族快速收敛至最优形式。
中文摘要 AI 辅助
在不可避免的近似方案中使用非微扰Wilson重整化群（FRG）方程，会产生依赖于粗粒化调节器选择的物理结果。根据最小敏感性原理（PMS），物理可观测量对调节器的这种依赖可以被最小化。对于基于Wetterich-Morris方程的1PI形式，我们提出在一组变量参数化的紧支撑多项式调节器空间内研究最优选择。我们使用有效平均作用的导数展开至四阶来测试该方法，将其应用于代表三维Ising普适类的标量场理论，并最小化异常维度对调节器的依赖。在四阶，我们发现临界指数的显著修正，与之前的单参数分析相比，改善了预测。我们还观察到，随着少量参数的逐步引入，紧致调节器族迅速收敛到最优函数形式。
英文摘要
The use of nonperturbative Wilsonian functional renormalization group (FRG) equations within an unavoidable approximation scheme produces physical results that depend on the choice of the coarse-graining regulator. This dependence of physical observables on the regulator can be minimized according to the principle of minimal sensitivity (PMS). For the 1PI formulation based on the Wetterich-Morris equation, we propose to investigate the optimal choice within a space of compactly supported polynomial regulators parametrized by a set of variables. We test this approach using the derivative expansion of the effective average action up to fourth order, applying it to the scalar field theory representing the three-dimensional Ising universality class and minimizing the dependence of the anomalous dimension on the regulator. At fourth order, we find appreciable corrections to the critical exponents that improve the predictions, compared to previous one parameter analyses. We also observe families of compact regulators that rapidly converge towards an optimal functional form as a small number of parameters is progressively introduced.
发表机构
- Ca’ Foscari University of Venice（威尼斯大学）
- Universidad de la República（乌拉圭共和国大学）
- INFN, Sezione di Bologna（意大利国家核物理研究所博洛尼部分所）
机构由 AI 辅助整理，请以论文原文为准。
