Renormalization group trajectories between two fixed points

Details Renormalization group trajectories between two fixed points Renormalization group trajectories between two fixed points

2009-10-06

arxiv.org/abs/0910.1063v1

Physics

Mathematical Physics

6 pages. Contribution to the proceedings of the XVI International Congress on Mathematical Physics, Prague, August 3-8, 2009

Scientific paper

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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