Abstract

It is known from the literature that the Ising and Potts models in one dimension d=1 do not present phase transitions at finite temperature T, for any number of states q. However, in  two  dimension d=2 there  are  a  second-order  phase  transition  and  a  first-order transition for q≤4 and q≥5, respectively. On directed Barabási-Albert networks, the Potts model with q=2 states (Ising model) no presents a phase transition. On the other hand, the  Potts  with q=3 presents a first-order phase transition well defined on these networks. This behavior is different from the Potts model with q=2 and 3 states on a square lattice where the phase transition is of the second-order. Here, we will briefly discuss the critical behavior of the Potts model on directed complex networks as the Barabási-Albert network also known as free scale networks.

Keywords

potts, networks, spins, ising model, scale networks, square lattice, two dimension, temperature, elementary models, statistical physics