Complex-temperature singularities of the susceptibility in the d = 2 Ising model

We report new results on complex-temperature singularities of the susceptibility χ of the 2D Ising model. We give a unified treatment of both the physical critical point and the singularity at u = u₃ = -1, which yields the relation γ′_s = 2(γ′ - 1). Using exact results, we show that universality is violated at the singularity u = -1 and discuss the reasons. We also show that certain exponent relations are violated at this point. The behavior of χ is analyzed as u = -1 is approached from the symmetric PM phase and from the FM and AFM phases.