Antiphase phenomena in 2d ising square lattice

Abstract

Monte Carlo simulations of the two dimensional Ising model were carried out to determine the impact of Antiphase Boundaries (APBs) in some thermodynamic functions of the system. We considered several lattice sizes and sometimes both Ferromagnetic (FM) and Antiferromagnetic (AFM) interactions for the same lattice. The analysis of the curves obtained shows that APBs appears only in AFM interaction and their effect is the creation of an energy gap
that prevents the system from reaching the ground state. This happens only in lattices with odd linear size L (L = 9, 15, 31 …). However, these boundaries do not change the critical temperature of the Antiferromagnetic/Paramagnetic (AFM/PARA) phase transition which remains approximately at 2.26 (in unit of J/kB). Nevertheless, they impose on the curve of the specific heat a jittery behaviour as a function of the temperature and with no clear peak as opposed to the case of even L (L = 16 ,20, 48,…) where there is a clear peak and a smooth curve. There is also a fluctuating magnetization around the value zero at low temperature (AFM phase). We show that this energy gap is proportional to 1/L where L is the linear size of the lattice, thus this gap should vanish if L becomes high. A similarity has been established with the role played by APB in some crystal structures and more especially in the binary alloys that are moreover described by the Ising model.