Anisotropic square lattice Potts ferromagnet: renormalisation group treatment
- 1 September 1982
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 15 (9) , 2865-2877
- https://doi.org/10.1088/0305-4470/15/9/035
Abstract
The choice of a convenient self-dual cell within a real space renormalisation group framework enables a satisfactory treatment of the anisotropic square lattice q-state Potts ferromagnet criticality. The exact critical frontier and dimensionality crossover exponent Hf as well as the expected universality behaviour (renormalisation flow sense) are recovered for any linear scaling factor b and all values of q(q<or=4). The b=2 and b=3 approximate correlation length critical exponent nu is calculated for all values of q and compared with the den Nijs conjecture. The same calculation is performed, for all values of b for the exponent nu (d=1) associated with the one-dimensional limit and the exact result nu (d=1)=1 is recovered in the limit b to infinity .Keywords
This publication has 23 references indexed in Scilit:
- Self-dual cluster renormalisation-group approach for the square lattice Ising model: specific heat and magnetisationJournal of Physics C: Solid State Physics, 1981
- Renormalisation group treatment of bond percolation in anisotropic and 'inhomogeneous' planar latticesJournal of Physics C: Solid State Physics, 1981
- Critical exponents of two-dimensional Potts and bond percolation modelsJournal of Physics A: General Physics, 1981
- Remarks on the Percolation Problem in Anisotropic SystemsProgress of Theoretical Physics, 1979
- Percolation in Anisotropic Systems: -- Real-Space Renormalization Group --Progress of Theoretical Physics, 1979
- Exact critical surface of the s-state Potts model with anisotropic interactions on the triangular and honeycomb latticesJournal of Physics A: General Physics, 1978
- Triangular Potts model at its transition temperature, and related modelsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978
- Notes on Migdal's recursion formulasAnnals of Physics, 1976
- High-temperature series study of the q-component Potts model in two and three dimensionsJournal of Physics A: General Physics, 1975
- Potts model at the critical temperatureJournal of Physics C: Solid State Physics, 1973