Frustrations and Ordering in Magnetic Systems of Various Dimensions

Based on the exact and numerical calculations within the Ising and Potts models on lattices of various types and dimensions (one-dimensional, square, triangular, hexagonal, kagome, simple cubic, and body-centered cubic), magnetic orderings, phase transitions, and frustrations were investigated, taking into account the exchange interactions between magnetic moments at the nearest and next-nearest nodes and an external magnetic field. The causes of the occurrence of frustrations are found, and the essential features of the behavior of frustrated systems that distinguish them from the nonfrustrated systems are determined.