Phase diagrams and crossover in spatially anisotropic d=3 Ising, XY magnetic, and percolation systems: Exact renormalization-group solutions of hierarchical models

Erbas A., Tuncer A., Yucesoy B., Berker A.

PHYSICAL REVIEW E, vol.72, no.2, 2005 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 2
  • Publication Date: 2005
  • Doi Number: 10.1103/physreve.72.026129
  • Journal Name: PHYSICAL REVIEW E
  • Journal Indexes: Science Citation Index Expanded, Scopus


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 and XY magnetic models and percolation systems, including crossovers from algebraic order to true long-range order.