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Full-Text Articles in Physics
Exactly Soluble Ising Models On Hierarchical Lattices, Miron Kaufman, Robert B. Griffiths
Exactly Soluble Ising Models On Hierarchical Lattices, Miron Kaufman, Robert B. Griffiths
Miron Kaufman
Certain approximate renormalization-group recursion relations are exact for Ising models on special hierarchical lattices, as noted by Berker and Ostlund. These lattice models provide numerous examples of phase coexistence and critical points at finite temperatures, including cases of continuously varying critical exponents and phase transitions without phase coexistence. The lattices are, typically, quite inhomogeneous and may possess several inequivalent limits as infinite lattices.
Three-Component Model And Tricritical Points: A Renormalization-Group Study., Miron Kaufman, Robert B. Griffiths, Julia M. Yeomans, Michael E. Fisher
Three-Component Model And Tricritical Points: A Renormalization-Group Study., Miron Kaufman, Robert B. Griffiths, Julia M. Yeomans, Michael E. Fisher
Miron Kaufman
The global phase diagram for a three-component lattice gas or spin-one Ising model with general single-site and nearest-neighbor "ferromagnetic" interactions is worked out for twodimensional lattices using a Migdal-Kadanoff recursion relation. It differs in important qualitative respects from the corresponding mean-field phase diagram. The set of fixed points and flows provides the characteristic'phase diagrams of the three-state Potts multicritical point and the ordinary (n =1) tricritical point in a complete set of symmetry-breaking fields. The latter is associated, in this renormalization-group scheme, with seven distinct critical fixed points, a number which is surprisingly large.