Nonlocal conservation in the coupling field: effect on critical dynamics

We consider the critical dynamics of a system with an n-component nonconserved order parameter coupled to a conserved field with long-range diffusion. An exponent sigma characterizes the long-range transport, sigma = 2 being the known locally conserved case. With renormalization group calculations done up to one loop order, several regions are found with different values of the dynamic exponent z in the sigma-n plane. For n < 4, there are three regimes, I: nonuniversal, sigma dependent z, II: universal with z depending on n and III': conservation law irrelevant, z being equal to that in the nonconserved case. The known locally conserved case belongs to regions I and II.