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We prove the stability of the torus, and with suitable rescaling, hyperbolic space under the (two-loop) renormalization group flow for the nonlinear sigma model. To prove stability we use similar techniques to Guenther et al. (Commun. Anal. Geom. 10:741–777, 2002), where the stability of the torus under Ricci flow was first established. The main technical tool is maximal regularity theory.