A study of the magnetic behavior of a mixed Ising system on a square lattice, where spins σ=±1/2 are located on alternating sites with spins S=±3/2,±1/2, is presented. The change in the magnetic behavior of the system when empty sites are introduced in one of the sublattices or in both is analyzed. This system can be thought of as a site‐diluted ferrimagnet or as a system with nonmagnetic impurities. The Hamiltonian of the model contains an exchange interaction between nearest neighbors S–σ, next‐nearest‐neighbors σ–σ, and a crystal field. The dependence of the total magnetization, the sublattice magnetizations, and the specific heat, with dilution is calculated. It is found that the behavior of the critical and compensation temperatures is strongly affected by dilution and where it is located. There is critical dilution, above which the compensation temperature disappears.

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We employ the second order of the derivative expansion of the nonperturbative renormalization group to study cubic (Z 4 -symmetric) perturbations to the classical XY model in dimensionality d ∈ [2,4]. In d = 3 we provide accurate estimates of the eigenvalue y 4 corresponding to the leading irrelevant perturbation and follow the evolution of the physical picture upon reducing spatial dimensionality from d = 3 towards d = 2, where we approximately recover the onset of the Kosterlitz-Thouless physics. We analyze the interplay between the leading irrelevant eigenvalues related to O(2)-symmetric and Z 4 -symmetric perturbations and their approximate collapse for d → 2. We compare and discuss different implementations of the derivative expansion in cases involving one and two invariants of the corresponding symmetry group.