Critical dynamics, finite-size effects, and supersymmetry

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Abstract
In this article, I study critical dynamics of two geometrical models: the nonlinear σ model and the almost planar model. I show how, in the pure relaxational case, the supersymmetric formulation of the dynamics simplifies the proof of the renormalizability of these models and allows one to calculate more easily the renormalization constants. In particular, I recover the dynamical renormalization-group functions at two-loop order obtained previously. In addition, having in mind numerical-simulation applications, I perform some finite-size calculations.