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 (${J}_{\mathrm{xy}}>0$, ${J}_{z}<0$). From the two-spin correlation function (expanded to eighth order in inverse temperature), series for the direct and staggered susceptibilities $\ensuremath{\chi}$ and ${\ensuremath{\chi}}_{\mathrm{st}}$ are obtained which are exact in the external field. The critical line in the $H\ensuremath{-}T$ plane is located, and along it ${\ensuremath{\chi}}_{\mathrm{st}}$ appears to diverge with a constant 5/4 exponent ${\ensuremath{\chi}}_{\mathrm{st}}\ensuremath{\sim}{[T\ensuremath{-}{T}_{c}(H)]}^{\frac{\ensuremath{-}5}{4}}$, consistent with the universality or "smoothness" postulate. Particular attention is focused on behavior near the tricritical point, where the phase transition in the $H\ensuremath{-}T$ 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 $\overline{\ensuremath{\gamma}}$ defined by $\ensuremath{\chi}\ensuremath{\sim}{(T\ensuremath{-}{T}_{t})}^{\ensuremath{-}\overline{\ensuremath{\gamma}}}$ 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