Universality in the partially anisotropic three-dimensional Ising lattice

Abstract

Using transfer-matrix extended phenomenological renormalization-group methods the critical properties of spin-1/2 Ising model on a simple-cubic lattice with partly anisotropic coupling strengths ${\vec J}=(J',J',J)$ are studied. Universality of both fundamental critical exponents $y_t$ and $y_h$ is confirmed. It is shown that the critical finite-size scaling amplitude ratios $U=A_{χ^{(4)}}A_κ/A_χ^2$, $Y_1=A_{κ^{''}}/A_χ$, and $Y_2=A_{κ^{(4)}}/A_{χ^{(4)}}$ are independent of the lattice anisotropy parameter $Δ=J'/J$. By this for the last above invariant of the three-dimensional Ising universality class we give the first quantitative estimate: $Y_2\simeq2.013$ (shape $L\times L\times\infty$, periodic boundary conditions in both transverse directions).