Magnetocaloric Effect for a <i>Q</i>-Clock-Type System
In this work, we study the magnetocaloric effect (MCE) in a working substance corresponding to a square lattice of spins with <i>Q</i> possible orientations, known as the “<i>Q</i>-state clock model”. When the <i>Q</i>-state clock model has <inline-formula>&...
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2024-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/27/1/11 |
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| author | Michel Aguilera Sergio Pino-Alarcón Francisco J. Peña Eugenio E. Vogel Natalia Cortés Patricio Vargas |
| author_facet | Michel Aguilera Sergio Pino-Alarcón Francisco J. Peña Eugenio E. Vogel Natalia Cortés Patricio Vargas |
| author_sort | Michel Aguilera |
| collection | DOAJ |
| description | In this work, we study the magnetocaloric effect (MCE) in a working substance corresponding to a square lattice of spins with <i>Q</i> possible orientations, known as the “<i>Q</i>-state clock model”. When the <i>Q</i>-state clock model has <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mo>≥</mo><mn>5</mn></mrow></semantics></math></inline-formula> possible configurations, it presents the famous Berezinskii–Kosterlitz–Thouless (BKT) phase associated with vortex states. We calculate the thermodynamic quantities using Monte Carlo simulations for even <i>Q</i> numbers, ranging from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mo>=</mo><mn>8</mn></mrow></semantics></math></inline-formula> spin orientations per site in a lattice. We use lattices of different sizes with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mi>L</mi><mo>×</mo><mi>L</mi><mo>=</mo><msup><mn>8</mn><mn>2</mn></msup><mo>,</mo><msup><mn>16</mn><mn>2</mn></msup><mo>,</mo><msup><mn>32</mn><mn>2</mn></msup><mo>,</mo><msup><mn>64</mn><mn>2</mn></msup><mo>,</mo><mi>and</mi><mspace width="4pt"></mspace><msup><mn>128</mn><mn>2</mn></msup></mrow></semantics></math></inline-formula> sites, considering free boundary conditions and an external magnetic field varying between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mo>=</mo><mn>1.0</mn></mrow></semantics></math></inline-formula> in natural units of the system. By obtaining the entropy, it is possible to quantify the MCE through an isothermal process in which the external magnetic field on the spin system is varied. In particular, we find the values of <i>Q</i> that maximize the MCE depending on the lattice size and the magnetic phase transitions linked with the process. Given the broader relevance of the <i>Q</i>-state clock model in areas such as percolation theory, neural networks, and biological systems, where multi-state interactions are essential, our study provides a robust framework in applied quantum mechanics, statistical physics, and related fields. |
| format | Article |
| id | doaj-art-e625b7c0bc32406aa025aa4dcd714104 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-e625b7c0bc32406aa025aa4dcd7141042025-01-24T13:31:39ZengMDPI AGEntropy1099-43002024-12-012711110.3390/e27010011Magnetocaloric Effect for a <i>Q</i>-Clock-Type SystemMichel Aguilera0Sergio Pino-Alarcón1Francisco J. Peña2Eugenio E. Vogel3Natalia Cortés4Patricio Vargas5Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4950, Valparaíso 2373223, ChileDepartamento de Física, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso 2390123, ChileDepartamento de Física, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso 2390123, ChileDepartamento de Ciencias Físicas, Universidad de La Frontera, Casilla 54-D, Temuco 4811230, ChileInstituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica 1000000, ChileDepartamento de Física, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso 2390123, ChileIn this work, we study the magnetocaloric effect (MCE) in a working substance corresponding to a square lattice of spins with <i>Q</i> possible orientations, known as the “<i>Q</i>-state clock model”. When the <i>Q</i>-state clock model has <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mo>≥</mo><mn>5</mn></mrow></semantics></math></inline-formula> possible configurations, it presents the famous Berezinskii–Kosterlitz–Thouless (BKT) phase associated with vortex states. We calculate the thermodynamic quantities using Monte Carlo simulations for even <i>Q</i> numbers, ranging from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mo>=</mo><mn>8</mn></mrow></semantics></math></inline-formula> spin orientations per site in a lattice. We use lattices of different sizes with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mi>L</mi><mo>×</mo><mi>L</mi><mo>=</mo><msup><mn>8</mn><mn>2</mn></msup><mo>,</mo><msup><mn>16</mn><mn>2</mn></msup><mo>,</mo><msup><mn>32</mn><mn>2</mn></msup><mo>,</mo><msup><mn>64</mn><mn>2</mn></msup><mo>,</mo><mi>and</mi><mspace width="4pt"></mspace><msup><mn>128</mn><mn>2</mn></msup></mrow></semantics></math></inline-formula> sites, considering free boundary conditions and an external magnetic field varying between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mo>=</mo><mn>1.0</mn></mrow></semantics></math></inline-formula> in natural units of the system. By obtaining the entropy, it is possible to quantify the MCE through an isothermal process in which the external magnetic field on the spin system is varied. In particular, we find the values of <i>Q</i> that maximize the MCE depending on the lattice size and the magnetic phase transitions linked with the process. Given the broader relevance of the <i>Q</i>-state clock model in areas such as percolation theory, neural networks, and biological systems, where multi-state interactions are essential, our study provides a robust framework in applied quantum mechanics, statistical physics, and related fields.https://www.mdpi.com/1099-4300/27/1/11entropy<i>Q</i>-clockmagnetocaloric |
| spellingShingle | Michel Aguilera Sergio Pino-Alarcón Francisco J. Peña Eugenio E. Vogel Natalia Cortés Patricio Vargas Magnetocaloric Effect for a <i>Q</i>-Clock-Type System Entropy entropy <i>Q</i>-clock magnetocaloric |
| title | Magnetocaloric Effect for a <i>Q</i>-Clock-Type System |
| title_full | Magnetocaloric Effect for a <i>Q</i>-Clock-Type System |
| title_fullStr | Magnetocaloric Effect for a <i>Q</i>-Clock-Type System |
| title_full_unstemmed | Magnetocaloric Effect for a <i>Q</i>-Clock-Type System |
| title_short | Magnetocaloric Effect for a <i>Q</i>-Clock-Type System |
| title_sort | magnetocaloric effect for a i q i clock type system |
| topic | entropy <i>Q</i>-clock magnetocaloric |
| url | https://www.mdpi.com/1099-4300/27/1/11 |
| work_keys_str_mv | AT michelaguilera magnetocaloriceffectforaiqiclocktypesystem AT sergiopinoalarcon magnetocaloriceffectforaiqiclocktypesystem AT franciscojpena magnetocaloriceffectforaiqiclocktypesystem AT eugenioevogel magnetocaloriceffectforaiqiclocktypesystem AT nataliacortes magnetocaloriceffectforaiqiclocktypesystem AT patriciovargas magnetocaloriceffectforaiqiclocktypesystem |