The $H$ model of critical dynamics: A proof of the multiplicative renormalizability of the simplified $H_0$ model

For the $H_0$ model of critical dynamics, which is obtained from the usual $H$ model by omitting the term with the velocity derivative $\partial_tv$, renormalization multiplicity is proved, and its connection with the statistics is shown. In the proof, a universal general scheme is formulated that can be used to prove similar statements for any model of critical dynamics.