Frustrations and Phase Transitions in Low-Dimensional Magnetic Systems

Abstract

We studied magnetic orderings and frustrations on 1D chain and 2D lattices: square, triangular, kagome, and hexagonal in the Ising, 3-state Potts and standard 4-state Potts models. The spins interrelate with one another via the nearest-neighbor, the next-nearest-neighbor or the third-neighbor exchange interactions and by an external magnetic field. For problem solving we mainly calculated the entropy and specific heat using the rigorous analytical solutions for maximum eigenvalue of Kramers-Wannier transfer-matrix and exploiting computer simulation, par excellence, by Wang-Landau algorithm. Whether a system is ordered or frustrated is related to the signs and values of exchange interactions. An external magnetic field may both favor the ordering of a system and create frustrations. With the help of calculations of the entropy, the specific heat and magnetic parameters, we obtained the points and ranges of frustrations, the frustration fields and the phase transition points. The results obtained also show that the same exchange interactions my either be competing or noncompeting which depends on the topology of a lattice.