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

摘要

Hierarchical lattices that constitute spatially anisotropic systems areintroduced. These lattices provide exact solutions for hierarchical models and,simultaneously, approximate solutions for uniaxially or fully anisotropic d=3physical 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, includingcrossovers from algebraic order to true long-range order.