Dynamic renormalization-group of a nonlocal φ4 model and critical behavior of some doped uniaxial ferromagnets

The critical behavior in the doped uniaxial systems depends upon the impurity concentration and is found to be nonuniversal. To model this behavior, we present a dynamic renormalization-group (RG) analysis at one-loop order for a $\phi^4$ model with nonlocal interactions, characterized by the long-range exponent $\sigma$. 
RG flow equations and the associated fixed points are determined, whose stability depends on both the spatial dimension $d$ and the exponent $\sigma.$ Numerical solutions show a linear shift of the fixed points as a function of $\sigma$ in three dimensions. Our calculations for the critical exponents anticipate the trend of the susceptibility exponent $\gamma$ as observed in experiments on some doped uniaxial ferromagnets. We propose dynamic universality classes for these systems, which require experimental confirmation.