Despite its simplicity as a model of a physical system, the Potts model is useful as a model system for the study of phase transitions. For example, for the standard ferromagnetic Potts model in 2 d , a phase transition exists for all real values q ≥ ≥ 1 , with the critical point at β β J = log ⁡ ⁡ ( 1 + q ) . The phase transition is continuous (second order) for 1 ≤ ≤ q ≤ ≤ 4 and discontinuous (first order) for q > 4 .