Universality in the partially anisotropic three-dimensional Ising lattice

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 $U=A_{\chi^{(4)}}A_\kappa/A_\chi^2$, $Y_1=A_{\kappa^{''}}/A_\chi$, and $Y_2=A_{\kappa^{(4)}}/A_{\chi^{(4)}}$ are independent of the lattice anisotropy parameter $\Delta=J'/J$. 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).Comment: 11 pages in latex; no figure

Critical temperature of a fully anisotropic three-dimensional Ising model

The critical temperature of a three-dimensional Ising model on a simple cubic lattice with different coupling strengths along all three spatial directions is calculated via the transfer matrix method and a finite size scaling for L x L oo clusters (L=2 and 3). The results obtained are compared with available calculations. An exact analytical solution is found for the 2 x 2 oo Ising chain with fully anisotropic interactions (arbitrary J_x, J_y and J_z).Comment: 17 pages in tex using preprint.sty for IOP journals, no figure

Double Potts chain and exact results for some two-dimensional models

A closed-form exact analytical solution for the q-state Potts model on a ladder 2 x oo with arbitrary two-, three-, and four-site interactions in a unit cell is presented. Using the obtained solution it is shown that the finite-size internal energy equation yields an accurate value of the critical temperature for the triangular Potts lattice with three-site interactions in alternate triangular faces. It is argued that the above equation is exact at least for self-dual models on isotropic lattices.Comment: 13 pages in latex and 2 ps figures. preprint ICTP IC/2000/176; ZhETF 120 (2001) (in press

Hyperuniversality of Fully Anisotropic Three-Dimensional Ising Model

For the fully anisotropic simple-cubic Ising lattice, the critical finite-size scaling amplitudes of both the spin-spin and energy-energy inverse correlation lengths and the singular part of the reduced free-energy density are calculated by the transfer-matrix method and a finite-size scaling for cyclic L x L x oo clusters with L=3 and 4. Analysis of the data obtained shows that the ratios and the directional geometric means of above amplitudes are universal.Comment: RevTeX 3.0, 24 pages, 2 figures upon request, accepted for publication in Phys. Rev.