Lattice-Dimensionality Crossover Effects in Quasi-d-Dimensional Magnetic Materials

We show that lattice-dimensionality crossover phenomena may be usefully analyzed by expansions in $R=\frac{J^{\prime }}{J}$, where $J$ and $J^{\prime }$ are the interaction constants in $d$ and $3-d$ lattice directions ($d=1\mathrm{} or 2$). The nature of the crossover phenomena is predicted to depend on the thermodynamic function considered, on $\mathrm{sgn}{J}^{\prime }$, and on $\mathrm{sgn}J$. Comparison with experiment confirms our predictions, and we present the first unambiguous experimental demonstration of crossover in the ferromagnetic susceptibility.