High-Temperature-Series Study of Models Displaying Tricritical Behavior. I. Ferromagnetic Planes Coupled Antiferromagnetically

Abstract

We introduce two Ising models which exhibit tricritical behavior. Their properties are studied in the presence of a nonzero external magnetic field using the method of high-temperature-series expansions. Both models may simulate some features of metamagnetic materials such as Fe${\mathrm{Cl}}_2$ or dysprosium aluminum garnet (DAG). In Paper I we treat the first model, called the "meta" model, which incorporates in-plane ferromagnetic and between-plane antiferromagnetic interactions ($J_{\mathrm{xy}}>0\mathrm{}$, $J_z<0\mathrm{}$). From the two-spin correlation function (expanded to eighth order in inverse temperature), series for the direct and staggered susceptibilities $\chi$ and ${\chi }_{\mathrm{st}}$ are obtained which are exact in the external field. The critical line in the $H-T$ plane is located, and along it ${\chi }_{\mathrm{st}}$ appears to diverge with a constant 5/4 exponent ${\chi }_{\mathrm{st}}\sim {[T-T_c\mathrm{}(H\left)\right]}^{\frac{-5\mathrm{}}{4}}$, consistent with the universality or "smoothness" postulate. Particular attention is focused on behavior near the tricritical point, where the phase transition in the $H-T$ plane changes from second to first order and where the critical-point exponents may be expected to take on a new set of values. At the tricritical point ($T_t$, $H_t$), the tricritical susceptibility exponent $\overline{\gamma }$ defined by $\chi \sim {(T-T_t)}^{-\overline{\gamma }}$ is estimated to be 1/2. The second model is analyzed in Paper II; there we also present the implications of our results for both models in the light of the scaling hypothesis for tricritical points