Spatially Anisotropic d=3 Ising, XY Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of Hierarchical Models

Hierarchical lattices that constitute spatially anisotropic systems are introduced. These lattices provide exact solutions for hierarchical models and, simultaneously, approximate solutions for uniaxially or fully anisotropic $d=3$ physical models. The global phase diagrams, with $d=2$ and $d=1$ to $d=3 $ crossovers, are obtained for Ising, XY magnetic models and percolation systems, including crossovers from algebraic order to true long-range order.$^1$ Our approach has been applied to spatially anisotropic $d=3$ tJ models of electronic conduction.$^2$\\ 1. A. Erba\c{s}, A. Tuncer, B. Y\"ucesoy, and A.N. Berker, Phys. Rev. E {\bf 72}, 026129 (2005).\\ 2. M. Hinczewski and A.N. Berker, cond-mat/0504741.