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

Abstract

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 = H c) point, where H c is the critical field at zero temperature, and at the ( T = 0, H = 0) point. Thermal exponents Y T are also calculated for arbitrary q along the critical lines.