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 $\vec{J}=(J^{\prime },J^{\prime },J)$ 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 $U=A_{{\chi }^{(4)}}{A}_{\kappa }/A_{\chi }^2$, $Y_1=A_{{\kappa }^{{}^{\prime \prime }}}/A_{\chi }$, and $Y_2=A_{{\kappa }^{(4)}}/A_{{\chi }^{(4)}}$ are independent of the lattice anisotropy parameter $\Delta =J^{\prime }/J$. By this for the last above invariant of the three-dimensional Ising universality class we give the first quantitative estimate: $Y_2\simeq 2.013$ (shape $L\times L\times \infty$, periodic boundary conditions in both transverse directions).

11 pages in latex; no figures

References in corpus (1)

• Critical Phenomena and Renormalization-Group Theory

Cited by in corpus (1)

• Extended scaling behavior of the spatially-anisotropic classical XY model in the crossover from three to two dimensions