The Ferromagnetic Potts model under an external magnetic field: an exact renormalization group approach

摘要

The q-state ferromagnetic Potts model under a non-zero magnetic field coupledwith the 0^th Potts state was investigated by an exact real-spacerenormalization group approach. The model was defined on a family of diamondhierarchical lattices of several fractal dimensions d_F. On these lattices, therenormalization group transformations became exact for such a model when acorrelation coupling that singles out the 0^th Potts state was included in theHamiltonian. The rich criticality presented by the model with q=3 and d_F=2 wasfully analyzed. Apart from the Potts criticality for the zero field, anIsing-like phase transition was found whenever the system was submitted to astrong reverse magnetic field. Unusual characteristics such as cusps anddimensional reduction were observed on the critical surface.