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Phase transitions are ubiquitous phenomena, exemplified by the melting of iceand spontaneous magnetization of magnetic material. In general, a phasetransition is associated with a symmetry breaking of a system; occurs due tothe competition between coupling interaction and external fields such asthermal energy. If the phase transition occurs with no latent heat, the systemexperiences continuous transition, also known as second order phase transition.The ferromagnetic $q$-state Potts model with $r$ extra invisible states,introduced by Tamura, Tanaka, and Kawashima [Prog. Theor. Phys. 124, 381(2010)], is studied by using the Wang-Landau method. The density of statesdifference (DOSD), $\ln g(E +\Delta E) - \ln g(E)$, is used to investigate theorder of the phase transition and examine the critical value of $r$ changingthe second to the first order transition.

Probing phase transition order of $q$-state Potts models using Wang-Landau Algorithm