Phase structure of Ising models at complex temperature

This work explores continuation of phases and phase transtions in statistical sums of planar Ising models to complex couplings -- temperature and field. We use a combination of analytic and numerical techniques, based on tensor network formulations of renormalization group (TRG and SRG) to access the regimes of phase space displaying novel modulated correlations and entirely out of reach of standard monte carlo methods. We also study and improve convergence and stability properties of tensor renormalization methods.