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

The $q$-state ferromagnetic Potts model under a nonzero magnetic field coupled with the zeroth Potts state was investigated by an exact real-space renormalization group approach. The model was defined on a family of diamond hierarchical lattices of several fractal dimensions ${d}_{F}$. On these lattices, the renormalization group transformations became exact for such a model when a correlation coupling that singles out the zeroth Potts state was included in the Hamiltonian. The rich criticality presented by the model with $q=3$ and ${d}_{F}=2$ was fully analyzed. Apart from the Potts criticality for the zero field, an Ising-like phase transition was found whenever the system was submitted to a strong reverse magnetic field. Unusual characteristics such as cusps and dimensional reduction were observed on the critical surface.

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