Abstract
The q-state ferromagnetic Potts model (FPM) and antiferromagnetic Potts model (APM) are solved on Bethe lattices for all values of the external magnetic field and temperature. The exact expressions of all thermodynamic functions of interest in the FPM and APM are calculated. The authors find the complete phase diagrams for both systems. In the FPM there are first-order phase transitions at the critical point for every q>2. In the APM they find second-order phase transitions along a critical line for every q>or=2.
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