Change in the order of a phase transition in the two-dimensional Potts model with equivalent neighbors

Two-dimensional (2D) Potts model is a classical example when the symmetry of the order parameter controls the order of a phase transition: on a square lattice with nearest-neighbors interaction, when the number of states q is less than or equal to 4, the second-order phase transition is observed, while for q>4 the first-order phase transition occurs. Recent research shows that even when the number of states is fixed, increasing the interaction range allows one to reach the point where the order of the phase transition changes. I focus on a q=3 2D Potts model and, from the analysis of the partition-function zeros, locate the number of interacting neighbors that change the order of the phase transition.