Entropy and Mutability for the q-State Clock Model in Small Systems
Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso 2340000, Chile
Centro para el Desarrollo de la Nanociencia y la Nanotecnología, CEDENNA, Santiago 8320000, Chile
Departamento de Ciencias Físicas, Universidad de La Frontera, Temuco 4811230, Chile
Author to whom correspondence should be addressed.
Received: 10 November 2018 / Revised: 27 November 2018 / Accepted: 3 December 2018 / Published: 6 December 2018
In this paper, we revisit the q
-state clock model for small systems. We present results for the thermodynamics of the q
-state clock model for values from
for small square lattices of
, with L ranging from
with free-boundary conditions. Energy, specific heat, entropy, and magnetization were measured. We found that the Berezinskii–Kosterlitz–Thouless (BKT)-like transition appears for
, regardless of lattice size, while this transition at
is lost for
, the BKT transition is never present. We present the phase diagram in terms of q
that shows the transition from the ferromagnetic (FM) to the paramagnetic (PM) phases at the critical temperature
for small systems, and the transition changes such that it is from the FM to the BKT phase for larger systems, while a second phase transition between the BKT and the PM phases occurs at
. We also show that the magnetic phases are well characterized by the two-dimensional (2D) distribution of the magnetization values. We made use of this opportunity to carry out an information theory analysis of the time series obtained from Monte Carlo simulations. In particular, we calculated the phenomenological mutability and diversity functions. Diversity characterizes the phase transitions, but the phases are less detectable as q
increases. Free boundary conditions were used to better mimic the reality of small systems (far from any thermodynamic limit). The role of size is discussed.
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MDPI and ACS Style
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 OA, Vargas P, Peña FJ, Saravia G, Vogel EE. Entropy and Mutability for the q-State Clock Model in Small Systems. Entropy. 2018; 20(12):933.
Negrete, Oscar A.; Vargas, Patricio; Peña, Francisco J.; Saravia, Gonzalo; Vogel, Eugenio E. 2018. "Entropy and Mutability for the q-State Clock Model in Small Systems." Entropy 20, no. 12: 933.
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