The one-dimensional spin-1/2 ANNNI model in non-commuting magnetic fields
Adekunle Moses Adegoke
- In this thesis we have investigated the one-dimensional spin-1/2 Axial Next Nearest Neighbour Ising (ANNNI) model in non-commuting magnetic fields. As a starting point we obtained an estimate of the phase diagram of the model by treating the spins as classical vectors. This was followed by an investigation of the zero temperature ground state of the one-dimensional spin-1/2 ANNNI model in a longitudinal magnetic field. By using the symmetries of the Hamiltonian, we were able to diagonalize the longitudinal ANNNI model exactly. We found that there are four different possible ground state configurations for the longitudinal ANNNI model, in the thermodynamic limit. Rayleigh Schroedinger perturbation series for the ground state energy of the ANNNI model in non-commuting fields were then developed in each of the four ordered regions. Order parameters and the associated susceptibilities as well as specific heats were calculated. By application of the finite-size scaling technique it was possible to obtain the phase boundaries of the model numerically. For certain limits of the full Hamiltonian we compared the obtained results with the existing literature and we got good agreement.