Frustrations and Phase Transitions in Low-Dimensional Magnetic Systems

Abstract

The phenomena of frustrations appearance and suppression of phase transition or, on the contrary, the phase transition appearance and suppression of frustrations are studied on the base of exact solutions for 1D 3-state [1], 4-state standard [2] Potts models and the Ising model [3] with allowance for the interactions between nearest J and next-nearest neighbors J'. We also studied these phenomena in the Ising model on 2D triangular, honeycomb, and kagome lattices, using the exact analytical solutions for maximum eigenvalue of Kramers-Wannier transfer matrix [4] и [5]. In 1D case we mainly used the analytical expressions for spin-spin correlation functions and formulas for entropy and binding energy, while in 2D case, specific heat, entropy, and binding energy expressed through the maximum eigenvalue of Kramers-Wannier transfer matrix were used.