We investigate the Sherrington–Kirkpatrick (SK) model with spin-S, including S=∞, in a framework of the replica method. We obtain replica symmetric (RS) solutions and one- and two-step replica symmetry breaking (RSB) solutions by using the Parisi scheme, after verifying de Almeida and...

We write the exact renormalization-group recursion relations for nearest-neighbor ferromagnetic Ising models on Migdal–Kadanoff hierarchical lattices with a distribution of aperiodic exchange interactions according to a class of substitutional sequences. For small geometric fluctuations, the...

The phase diagrams of the semi-infinite Ising ferromagnet with decorated magnetic (spin-S) and nonmagnetic atoms on the surface are investigated within the framework of the effective-field theory. In particular, the critical properties of the special point in the surface phase diagram are...

The magnetic properties of diluted mixed-spin-12 and spin-1 Ising magnetic systems with crystal-field interactions on a honeycomb lattice (z = 3) are investigated by using the effective-field theory with correlations. The phase diagrams are given for both ferromagnet and ferrimagnet. The...