两个不动点之间的重整化群轨道
Renormalization group trajectories between two fixed points
摘要：
本文报道了我们最近对Brydges，Mitter和Scoppola（BMS）提出的具有修正传播子的三维Φ-4模型在两个不动点之间的完全重整化群轨道的严格构造.这些是离散的临界轨迹，连接紫外高斯不动点的非平凡BMS红外不动点，这是一个类似的威尔逊-费舍尔不动点。在不使用层次近似的情况下，严格地、非微扰地定义了重整化群映射。在适当的Banach空间序列，其中一个扰动的非线性一维迭代的轨迹构造的不动点参数。
英文摘要：
We report on our recent rigorous construction of complete renormalization group trajectories between two fixed points for the three-dimensional phi-four model with modified propagator considered by Brydges, Mitter and Scoppola (BMS). These are discrete critical trajectories which connect the ultraviolet Gaussian fixed point to the nontrivial BMS infrared fixed point which is an analogue of the Wilson--Fisher fixed point. The renormalization group map is defined rigorously and nonperturbatively, without using the hierarchical approximation. The trajectories are constructed by a fixed point argument in a suitable Banach space of sequences, where one perturbs a nonlinear one-dimensional iteration.
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