Mapping between hierarchical lattices by renormalisation and duality
- 11 July 1987
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 20 (10) , 2961-2971
- https://doi.org/10.1088/0305-4470/20/10/038
Abstract
The renormalisation group scheme of Migdal (1976) and Kadanoff (1976) is applied to a ferromagnetic Potts model on two hierarchical lattices: in the two cases the renormalisation transformation is split into two elementary processes (parallel bonds or series bonds) and each lattice can be mapped onto the other one. It is then easy to deduce the characteristic parameters (critical exponents, repulsive fixed points, etc) of one lattice from those of the other lattice. Moreover the classical geometrical duality offers a third possibility of mapping and the relationship between the renormalisation and the duality methods is presented in the peculiar case of a two-dimensional lattice.Keywords
This publication has 18 references indexed in Scilit:
- Duality and Potts critical amplitudes on a class of hierarchical latticesPhysical Review B, 1984
- Oscillatory critical amplitudes in hierarchical modelsCommunications in Mathematical Physics, 1984
- Fractal structure of zeros in hierarchical modelsJournal of Statistical Physics, 1983
- The Migdal-Kadanoff approximation: optimisation, generalisation, Ising model in external fields and the Migdal-Kadanoff hierarchiesJournal of Physics A: General Physics, 1983
- Renormalisation groups with periodic and aperiodic orbitsJournal of Physics A: General Physics, 1983
- Hierarchical q-state Potts models with periodic and aperiodic renormalization group trajectoriesPhysics Letters A, 1983
- Spin systems on hierarchical lattices. Introduction and thermodynamic limitPhysical Review B, 1982
- Infinite susceptibility at high temperatures in the Migdal-Kadanoff schemeJournal of Physics A: General Physics, 1982
- Exactly soluble Ising models on hierarchical latticesPhysical Review B, 1981
- Renormalisation-group calculations of finite systems: order parameter and specific heat for epitaxial orderingJournal of Physics C: Solid State Physics, 1979