ISING MODELS WITH N GREATER-THAN 1 - SERIES-EXPANSION APPROACH

We investigate the Ising model with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interactions on the square and body-centered-cubic lattices. For 0<J1J2<32 on the bcc lattice the model has two nontrivially degenerate ground states and has been conjectured to have XY (n=2) critical exponents. For J1J2=32 there are three degenerate ground states and Heisenberg critical exponents (n=3) are expected. We have obtained nine terms in the high-temperature expansion of the staggered susceptibility. For 0<J1J2<~1 we find γ=1.25 (n=1). At J1J2=32 the results are not conclusive, but γ=1.33 (n=2) is not ruled out by the series analysis whereas γ=1.4 (n=3) is not probable. Results for the square lattice are inconclusive. © 1979 The American Physical Society.