The $q$-state Potts model on a square lattice and in the presence of an external magnetic field that couples to only one state is studied by using extensive Monte Carlo simulations. A hybrid algorithm that combines the single spin-flip Metropolis method with Wolff cluster updates is employed. Single-histogram reweighting techniques and the field-mixing approach are also used to obtain the corresponding universal probability distributions. By analyzing the finite-size scaling behavior of the order parameters and universal probability distributions, the phase diagram in the temperature–versus–external field plane is obtained in the thermodynamic limit for some values of state $q\ge 5$. For positive fields and higher values of $q$, there is a clear first-order transition line that starts at the zero-field transition point and ends at an isolated critical point, which is in the two-dimensional Ising universality class. As the value of state $q$ decreases, the corresponding critical field also decreases. The present results strongly suggest that the critical field vanishes when $q\to 5^{+}$. However, for negative fields, another first-order transition line occurs without any critical or multicritical behavior for $q\ge 6$. The special case with $q=5$ undergoes a weak first-order transition at zero field and a line of second-order transitions for negative fields. This second-order transition line is in the same universality class as the $q=4$ Potts model.

Close

PrevNext

View figure in article

• Classical statistical mechanics
• Critical phenomena
• Phase diagrams
• Phase transitions