COMPLEX-TEMPERATURE SINGULARITIES IN THE D=2 ISING-MODEL - TRIANGULARAND HONEYCOMB LATTICES

We study complex-temperature singularities of the Ising model on the t riangular and honeycomb lattices. We first discuss the complex-T phase s and their boundaries. From exact results, we determine the complex-T singularities in the specific heat and magnetization. For the triangu lar lattice we discuss the implications of the divergence of the magne tization at the point u = -1/3 (where u = z(2) = e(-4K)) and extend a previous study by Guttmann of the susceptibility at this point with th e use of differential approximants. For the honeycomb lattice, from an analysis of low-temperature series expansions, we have found evidence that the uniform and staggered susceptibilities <(chi)over bar> and < (chi)over bar>((a)) both have divergent singularities at z = -1 = z(e) , and our numerical values for the exponents are consistent with the h ypothesis that the exact values are gamma'(l) = gamma'(l,a) = 5/2. The critical amplitudes at this singularity were calculated. Using our ex act results for alpha' and beta together with numerical values for gam ma' from series analyses, we find that the exponent relation (alpha' 2 beta + gamma' = 2 is violated at z = -1 on the honeycomb lattice; t he right-hand side is consistent with being equal to 4 rather than 2. The connections of the critical exponents at these two singularities o n the triangular and honeycomb lattice are discussed.