Phase diagram of antiferromagnetic Potts model on the kagome lattice

Using the method of computer simulation, phase transitions of the two-dimensional antiferromagnetic Potts model with the number of spin states $q$ = 4 on the kagome lattice with interactions of the first $J_1$ and second $J_2$ neighbors were carried out. The studies were carried out for the magnitude of the exchange interaction of second neighbors in the range 0 $\le J_2\le$ 1. A phase diagram of the dependence of the critical temperature on the magnitude of interactions of second neighbors was constructed. An analysis of the nature of phase transitions was carried out. It was found that for values $J_2$ = 0 and 0.1 there is no phase transition in this model. It is shown that in the range 0.2 $\le J_2\le$ 1 a second-order phase transition is observed.