# Critical dynamics within the real-time fRG approach

arxiv（2023）

Abstract

The Schwinger-Keldysh functional renormalization group (fRG) developed in [1]
is employed to investigate critical dynamics related to a second-order phase
transition. The effective action of model A is expanded to the order of
$O(\partial^2)$ in the derivative expansion for the $O(N)$ symmetry. By solving
the fixed-point equations of effective potential and wave function, we obtain
static and dynamic critical exponents for different values of the spatial
dimension $d$ and the field component number $N$. It is found that one has $z
\geq 2$ in the whole range of $2\leq d\leq 4$ for the case of $N=1$, while in
the case of $N=4$ the dynamic critical exponent turns to $z < 2$ when the
dimension approach towards $d=2$.

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