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

Abstract

A magnetic system with intraplanar and interplanar interaction strengths $J$ and $\mathrm{RJ}$ is is treated. Rigorous relations are established concerning the first few derivatives with respect to $R$ of the susceptibility $\chi \mathrm{}\left(R\right)\mathrm{}$. Considering $\chi \mathrm{}\left(R\right)=b_0+b_{1}R+b_2{R}^2+\cdots$, we find $b_1$ and the order of magnitude of $b_2$. Hence we can predict when the system "crosses over" from $d$-dimensional to $d$-dimensional behavior (e.g., for quasi—two-dimensional systems, $d=2\mathrm{}$, $\overline{d}=3\mathrm{}$, while for quasi—one-dimensional systems, $d=1\mathrm{}$, $\overline{d}=3\mathrm{}$). These results also support scaling with respect to the anisotropy parameter $R$.