We calculate the relaxational dynamical critical behavior of systems of $O\left(n_{\parallel }\right)\oplus O\left(n_{\perp }\right)$ symmetry by renormalization group method within the minimal subtraction scheme in two-loop order. The three different bicritical static universality classes previously found for such systems correspond to three different dynamical universality classes within the static borderlines. The Heisenberg and the biconical fixed point lead to strong dynamic scaling whereas in the region of stability of the decoupled fixed point weak dynamic scaling holds. Due to the neighborhood of the stability border between the strong and the weak scaling dynamic fixed point to the dynamical stable fixed point a very small dynamic transient exponent of ${\omega }_v^{\mathcal{B}}=0.0044$ is present in the dynamics for the physically important case $n_{\parallel }=1$ and $n_{\perp }=2$ in $d=3$.

• Received 12 August 2008

DOI:https://doi.org/10.1103/PhysRevE.78.041125