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Entropy and Mutability for the q-State Clock Model in Small Systems.
Oscar A Negrete1, Patricio Vargas1,2, Francisco J Peña1
1Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso 2340000, Chile.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
The q-state clock model exhibits a Berezinskii-Kosterlitz-Thouless (BKT)-like transition for q > 5 in small systems. This transition is absent for q ≤ 4, and its presence depends on lattice size for q = 5.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Computational Physics
Background:
- The q-state clock model is a fundamental model in statistical mechanics.
- Understanding phase transitions in small systems is crucial for various physical phenomena.
- Previous studies often focused on the thermodynamic limit, neglecting finite-size effects.
Purpose of the Study:
- To investigate the thermodynamics and phase transitions of the q-state clock model in small systems.
- To determine the critical behavior and phase diagram as a function of q and lattice size.
- To analyze the role of free boundary conditions in small systems.
Main Methods:
- Monte Carlo simulations were employed to study the q-state clock model.
- Thermodynamic quantities such as energy, specific heat, entropy, and magnetization were measured.
- Information theory analysis, including diversity and mutability functions, was used to characterize phases.
Main Results:
- A Berezinskii-Kosterlitz-Thouless (BKT)-like transition was observed for q > 5, independent of lattice size.
- This BKT transition was absent for q ≤ 4 and sensitive to lattice size at q = 5.
- The phase diagram revealed transitions from ferromagnetic (FM) to paramagnetic (PM) or BKT phases, characterized by magnetization distributions.
Conclusions:
- The study clarifies the conditions under which BKT-like transitions occur in small q-state clock models.
- Free boundary conditions provide a more realistic approach for studying small systems.
- Information theory analysis offers a novel way to characterize phase transitions and their detectability.
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