Complex-temperature Ising model: Symmetry properties and behavior of correlation length and susceptibility

We derive symmetry properties of Ising models on general lattices under complex translations of inverse temperature. These are applied in particular to study correlation functions, and the susceptibility, χ, for complex temperatures. We determine the full set of complex-temperature points in the square-lattice Ising model where the correlation functions are not damped exponentially at large spin-spin separations. The complex-temperature behavior of χ is described by certain theorems and a Padé analysis of high-temperature series expansions. Finally, a new series expansion variable which incorporates the exact symmetry of χ is proposed.