  We study dimensional crossover in Ising systems at complex temperatures by
comparing three types of system: the infinite isotropic 2D Ising model; the
infinite anisotropic 2D Ising model; and Ising ladders with a finite number of
legs. In particular we present evidence, from both tensor-network calculations
and numerical evaluations based on the exact solution of the model, that the
infinite anisotropic 2D Ising model exhibits long-range spatially modulated
magnetization in certain regions of the complex-temperature plane. We discuss
the physics of the special unitary points that exists in the
complex-temperature plane, and their connections to the theory of quantum
information processing.
