Some Results Concerning the Crossover Behavior of Quasi—Two-Dimensional and Quasi—One-Dimensional Systems

A magnetic system with intraplanar and interplanar interaction strengths J and RJ is is treated. Rigorous relations are established concerning the first few derivatives with respect to R of the susceptibility χ(R). Considering χ(R)=b₀+b₁R+b₂R²+⋯, we find b₁ and the order of magnitude of b₂. Hence we can predict when the system "crosses over" from d-dimensional to d-dimensional behavior (e.g., for quasi---two-dimensional systems, $d=2$, d̄=3, while for quasi---one-dimensional systems, $d=1$, d̄=3). These results also support scaling with respect to the anisotropy parameter R.