Non-universal critical behaviour in mean-field theory of inhomogeneous systems

We consider the layered magnetic systems with inhomogeneous inter-layer couplings and study their critical properties within the framework of mean-field theory. We consider two kinds of distribution of the couplings: (i) quasi-periodic, according to the Fibonacci sequence and (ii) smoothly inhomogeneous, in which the couplings deviate from the bulk couplings by an amount of Al−2, where l measures the distance from a free surface. According to analytical and accurate numerical results the critical behaviour of both the problems is non-universal and the corresponding critical exponents are coupling dependent.