3-DIMENSIONAL AXIAL NEXT-NEAREST-NEIGHBOR ISING-MODEL - A SERIES INVESTIGATION

We have derived a twelfth-order, high-temperature series for the axial next-nearest-neighbor Ising (ANNNI) models on the fcc and the sc lattices, and we present detailed results for one of the fcc models. We have determined the phase boundaries of these models and located the Lifshitz point from the intersection of the phase boundary with the ''disorder'' line, where the maximum in the susceptibility chi(q) begins to occur at nonzero q signaling the onset of modulated correlations. As expected, the Lifshitz point appears to be an inflection point of the phase boundary. The effective susceptibility index shows the predicted universal values for definite regions of the parameter space, e.g., XY-like in the midrange modulated regime, with the expected smooth crossover near the multicritical points. Throughout the modulated regime from the Lifshitz point to the decoupling point, the variation in the critical wave vector shows only small deviations from mean-field predictions. Our best estimates for the Lifshitz-point indices, gamma-l = 1.62 +/- 0.12, 4-nu-l4 = 1.63 +/- 0.10, and alpha-l = 0.20 +/- 0.15, differ from previous estimates. We are confident that our estimates are more reliable not only because we have longer series for a close-packed lattice but also primarily because we have analyzed our series along the appropriate scaling direction.