Anisotropic square lattice Potts ferromagnet: renormalisation group treatment

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 .