Antiferromagnetic Potts model in a magnetic field: a finite size scaling study

The finite size scaling method is used to investigate the phase diagrams of the q-state antiferromagnetic Potts model in an external magnetic field on a square lattice. Critical lines where the system undergoes second-order phase transitions between ordered and disordered phases are found, which are in complete qualitative agreement with known results for q = 3. Also new unexpected features are found for q ⩾ 4 where the transition vanishes in the negative field region, while in the positive field region, as q increases, the critical line flattens out with increasing slopes both at the (T = 0, H = Hc) point, where Hc is the critical field at zero temperature, and at the (T = 0, H = 0) point. Thermal exponents YT are also calculated for arbitrary q along the critical lines.