New parameters and extensive methodology to describe the three phase transitions in the q-states clock model

In the q-state clock model the spin has q possible orientations in the plane so it can be understood as a generalization of the Ising model for which q=2. The Hamiltonian is then the scalar product of the neighboring spins mediated by the ferromagnetic exchange interaction J homogeneous through the square lattice with L´L=N spins. It is known that for q≤4 there is only one phase transition at a temperature T₁, over which the ferromagnetic phase is lost. Using global order parameters it has been previously established that for q≥5 this transitions moves steadily to lower temperatures as q increases [1]. For large L the appearing of the so called (Berezinskii–Kosterlitz–Thouless (BKT) phase characterized by vortex like structures is established, while a second transition to a disordered phase appears at a higher T₂ temperature. In the present paper we deeply characterize the nature of this second transition by means of new local order parameters. Surprisingly, an unexpected subtle transition appears at a temperature slightly over the second one (at T₃) requiring interpretation. This is resolved by considering pure and mixed ferromagnetic, vortex and paramagnetic phases as T increases requiring local order parameters and new methodology to better handle them. Thus, we include now information theory analysis by means of mutability and Shannon entropy characterization. Tendencies towards large N and q values are established.

[1] O.A. Negrete, P. Vargas, F. Peña, G. Saravia, and E.E. Vogel, Entropy 20, 933 (2018).