Negrete, O.A.; Vargas, P.; Peña, F.J.; Saravia, G.; Vogel, E.E. Entropy and Mutability for the q-State Clock Model in Small Systems. Entropy2018, 20, 933.
Negrete, O.A.; Vargas, P.; Peña, F.J.; Saravia, G.; Vogel, E.E. Entropy and Mutability for the q-State Clock Model in Small Systems. Entropy 2018, 20, 933.

Negrete, O.A.; Vargas, P.; Peña, F.J.; Saravia, G.; Vogel, E.E. Entropy and Mutability for the q-State Clock Model in Small Systems. Entropy2018, 20, 933.
Negrete, O.A.; Vargas, P.; Peña, F.J.; Saravia, G.; Vogel, E.E. Entropy and Mutability for the q-State Clock Model in Small Systems. Entropy 2018, 20, 933.

Abstract

In this paper, we revisit the q-states clock model for small systems. We present results for the thermodynamics of the q-states clock model from $q=2$ to $q=20$ for small square lattices $L \times L$, with L ranging from $L=3$ to $L=64$ with free-boundary conditions. Energy, specific heat, entropy and magnetization are measured. We found that the Berezinskii-Kosterlitz-Thouless (BKT)-like transition appears for $q>5$ regardless of lattice size, while the transition at $q=5$ is lost for $L<10$; for $q\leq 4$ the BKT transition is never present. We report the phase diagram in terms of $q$ showing the transition from the ferromagnetic (FM) to the paramagnetic (PM) phases at a critical temperature T$_1$ for small systems which turns into a transition from the FM to the BKT phase for larger systems, while a second phase transition between the BKT and the PM phases occurs at T$_2$. We also show that the magnetic phases are well characterized by the two dimensional (2D) distribution of the magnetization values. We make use of this opportunity to do an information theory analysis of the time series obtained from the Monte Carlo simulations. In particular, we calculate the phenomenological mutability and diversity functions. Diversity characterizes the phase transitions, but the phases are less detectable as $q$ increases. Free boundary conditions are used to better mimic the reality of small systems (far from any thermodynamic limit). The role of size is discussed.

Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.