32 research outputs found
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 are studied.
Universality of both fundamental critical exponents and is
confirmed. It is shown that the critical finite-size scaling amplitude ratios
, , and
are independent of the lattice anisotropy
parameter . By this for the last above invariant of the
three-dimensional Ising universality class we give the first quantitative
estimate: (shape , periodic boundary
conditions in both transverse directions).Comment: 11 pages in latex; 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
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
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.