The One-dimensional Spin-1/2 ANNNI Model in Two Magnetic Fields : continuous quantum phase transitions

We present results for the investigation of the one- dimensional spin-1/2 Axial Next Nearest Neighbour Ising (ANNNI) model in perpendicular magnetic fields. As a starting point we obtain an estimate of the phase diagram of the model by treating the spins as classical vectors. This is followed by an investigation of the ground state of the one- dimensional spin-1/2 ANNNI model in a longitudinal magnetic field. By using the symmetries of the Hamiltonian, we are able to do energy classification for the longitudinal ANNNI model. We find 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 are then developed in each of the four ordered regions. Order parameters and the associated susceptibilities as well as specific heats are calculated. By application of the finite-size scaling technique the phase boundaries of the model are obtained numerically. For certain limits of the full Hamiltonian we compare the obtained results with the existing literature.