Phases at complex temperature : spiral correlation functions and regions of Fisher zeros for Ising models

Abstract

In this thesis we analyse the Fisher zeros for various Ising models. We show that there is long-range spiral order on the contours of zeros for classical one-dimensional Ising chains and that there is an imaginary “latent heat” associated with crossing those contours. Then we can see how areas of Fisher zeros fill in as we turn the Ising chain into Ising ladders of different widths, which seems to contradict the standard analysis presented in the literature and can be attributed to a different approach to the thermodynamic limit. Finally, we report results on frustrated two-dimensional classical Ising lattices, in particular the triangular and the kagomé lattice, and the quantum Ising problem.