Phase Structure of Isotropic and Anisotropic Ising Models at Complex Couplings

In this work, we study the phase structures and phase transitions that arise in both the Isotropic and the Anisotropic Ising Models by analytically continuing away from real coupling – both temperature and field. In particular, we observe that away from real temperatures, Yang-Lee circle theorem indeed breaks down, even for the Isotropic Ising Model. We also observe symmetry breaking of the global minima of the free energy away from real temperatures in the high temperature phase. We use both analytical as well as numerical techniques based on Tensor Network formulations (Tensor Renormalization Group(TRG), Higher Order Tensor Renormalization Group(HOTRG)) to access these novel regimes in the phase space that is out of reach of standard Monte Carlo techniques.