High-Temperature-Series Study of Models Displaying Tricritical Behavior. II. A Nearest-Neighbor Ising Antiferromagnet with Next-Nearest-Neighbor Ferromagnetic Interactions

Abstract

The nnn model is an Ising model with nearest-neighbor antiferromagnetic interactions ($J_1<0\mathrm{}$) but also next-nearest-neighbor ferromagnetic exchange ($J_2>0\mathrm{}$). This model is analyzed in external magnetic field using the same techniques as applied to the meta model of Paper I. Again, the staggered susceptibility ${\chi }_{\mathrm{st}}$ appears to diverge along the critical line in the $H-T$ plane with a constant exponent ${\gamma }_{\mathrm{st}}=\frac{5}{4}$, consistent with the universality hypothesis. However, in contrast to the meta model, it is found that the direct susceptibility $\chi$ diverges at the tricritical point with an exponent $\overline{\gamma }\simeq \frac{1}{4}$. Implications of the scaling hypothesis at the tricritical point are discussed and the results for both the meta and nnn models are utilized to obtain the scaling power ${\overline{a}}_2$ corresponding to the "weak" direction (in the sense of Griffiths and Wheeler). Included in this discussion is the double-power-law form, predicted to hold within the crossover region by tricritical-point scaling.