Phase Transitions in the Transverse-field Ising Ladder

Abstract

In this thesis I have successfully recreated the results that describe the behavior of a transverse-field Ising chain. There is a phase transition when the parameter that controls the influence of the transverse field is one (that is: the factor in front of the transverse-field term and the interaction term are equally big). However, I could not determine exactly what the order parameter should be. Then for the transverse-field Ising ladder I have used perturbation theory in the parameter that controls the interaction between the chains. I have found that the phase transition doesn't change position, but that the ground state is a different state compared to the transverse-field Ising chain, when the transverse-field term is smaller than the interaction.