COMPLEX-TEMPERATURE SINGULARITIES OF THE SUSCEPTIBILITY IN THE D=2 ISING-MODEL .1. SQUARE LATTICE

We investigate the complex-temperature singularities of the susceptibility of the 2D Ising model on a square lattice. From an analysis of low-temperature series expansions, we find evidence that, as one approaches the point u = u(s) = -1 (where u = e(-4K)) from within the complex extensions of the FM or AFM phases, the susceptibility has a divergent singularity of the form chi similar to A(s)'(1 + u)-gamma(s)' with exponent v(s)' = 3/2. The critical amplitude A(s)' is calculated. Other critical exponents are found to be alpha(s)' = alpha(s) = 0 and beta(s) = 1/4, so that the scaling relation alpha(s)' + 2 beta(s) + gamma(s)' = 2 is satisfied. However, using exact results for beta(s) on the square, triangular, and honeycomb lattices, we show that universality is violated at this singularity: beta(s), is lattice-dependent. Finally, from an analysis of spin-spin correlation functions, we demonstrate that the correlation length and hence susceptibility are finite as one approaches the point u = -1 from within the symmetric phase. This is confirmed by an explicit study of high-temperature series expansions.