The Investigation of a Temperature and Field Characteristics of the One-dimensional Ising Model with Competing Exchange Interactions

Abstract

The high-efficient Wang-Landau and replica exchange algorithm of the Monte-Carlo method is used for the one-dimensional Ising model studying, with regards to the competing exchange interaction between the first, second and third nearest neighbors and external magnetic field. Using the Wang-Landau algorithm, the density of states is calculated, the ground state magnetic structures are determined and the temperature dependences of the various thermodynamic parameters, such as internal energy E, specific heat C, entropy S, magnetization m, susceptibility  etc. are calculated. It is shown how the ground state (state with minimal energy) of the system changes when applying an external magnetic field. The phase diagram is plotted and it is shown that, depending on the value of the external magnetic field, the system can be in phase I (has a structure +++ ---+++---...), in phase II (has a structure +++--+++--...), in phase III (all the spins are arranged along the magnetic field: +++++++++++...). A good agreement of the results obtained by the two completely different numerical methods is shown.