Otto Engine for the <i>q</i>-State Clock Model
This present work explores the performance of a thermal–magnetic engine of Otto type, considering as a working substance an effective interacting spin model corresponding to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><sema...
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MDPI AG
2022-02-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/2/268 |
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| author | Michel Angelo Aguilera Francisco José Peña Oscar Andrés Negrete Patricio Vargas |
| author_facet | Michel Angelo Aguilera Francisco José Peña Oscar Andrés Negrete Patricio Vargas |
| author_sort | Michel Angelo Aguilera |
| collection | DOAJ |
| description | This present work explores the performance of a thermal–magnetic engine of Otto type, considering as a working substance an effective interacting spin model corresponding to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>−</mo></mrow></semantics></math></inline-formula> state clock model. We obtain all the thermodynamic quantities for the <i>q</i> = 2, 4, 6, and 8 cases in a small lattice size (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>×</mo><mn>3</mn></mrow></semantics></math></inline-formula> with free boundary conditions) by using the exact partition function calculated from the energies of all the accessible microstates of the system. The extension to bigger lattices was performed using the mean-field approximation. Our results indicate that the total work extraction of the cycle is highest for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> case, while the performance for the Ising model (<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>) is the lowest of all cases studied. These results are strongly linked with the phase diagram of the working substance and the location of the cycle in the different magnetic phases present, where we find that the transition from a ferromagnetic to a paramagnetic phase extracts more work than one of the Berezinskii–Kosterlitz–Thouless to paramagnetic type. Additionally, as the size of the lattice increases, the extraction work is lower than smaller lattices for all values of <i>q</i> presented in this study. |
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| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T22:01:20Z |
| publishDate | 2022-02-01 |
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| spelling | doaj.art-32bceb2885634a7d887f1ba6498ab9e02023-11-23T19:48:40ZengMDPI AGEntropy1099-43002022-02-0124226810.3390/e24020268Otto Engine for the <i>q</i>-State Clock ModelMichel Angelo Aguilera0Francisco José Peña1Oscar Andrés Negrete2Patricio Vargas3Department of Physics, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso 2390123, ChileDepartment of Physics, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso 2390123, ChileDepartment of Physics, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso 2390123, ChileDepartment of Physics, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso 2390123, ChileThis present work explores the performance of a thermal–magnetic engine of Otto type, considering as a working substance an effective interacting spin model corresponding to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>−</mo></mrow></semantics></math></inline-formula> state clock model. We obtain all the thermodynamic quantities for the <i>q</i> = 2, 4, 6, and 8 cases in a small lattice size (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>×</mo><mn>3</mn></mrow></semantics></math></inline-formula> with free boundary conditions) by using the exact partition function calculated from the energies of all the accessible microstates of the system. The extension to bigger lattices was performed using the mean-field approximation. Our results indicate that the total work extraction of the cycle is highest for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> case, while the performance for the Ising model (<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>) is the lowest of all cases studied. These results are strongly linked with the phase diagram of the working substance and the location of the cycle in the different magnetic phases present, where we find that the transition from a ferromagnetic to a paramagnetic phase extracts more work than one of the Berezinskii–Kosterlitz–Thouless to paramagnetic type. Additionally, as the size of the lattice increases, the extraction work is lower than smaller lattices for all values of <i>q</i> presented in this study.https://www.mdpi.com/1099-4300/24/2/268<i>q</i>-state clock modelentropyBerezinskii–Kosterlitz–Thouless transitionOtto enginemean-field approximation |
| spellingShingle | Michel Angelo Aguilera Francisco José Peña Oscar Andrés Negrete Patricio Vargas Otto Engine for the <i>q</i>-State Clock Model Entropy <i>q</i>-state clock model entropy Berezinskii–Kosterlitz–Thouless transition Otto engine mean-field approximation |
| title | Otto Engine for the <i>q</i>-State Clock Model |
| title_full | Otto Engine for the <i>q</i>-State Clock Model |
| title_fullStr | Otto Engine for the <i>q</i>-State Clock Model |
| title_full_unstemmed | Otto Engine for the <i>q</i>-State Clock Model |
| title_short | Otto Engine for the <i>q</i>-State Clock Model |
| title_sort | otto engine for the i q i state clock model |
| topic | <i>q</i>-state clock model entropy Berezinskii–Kosterlitz–Thouless transition Otto engine mean-field approximation |
| url | https://www.mdpi.com/1099-4300/24/2/268 |
| work_keys_str_mv | AT michelangeloaguilera ottoenginefortheiqistateclockmodel AT franciscojosepena ottoenginefortheiqistateclockmodel AT oscarandresnegrete ottoenginefortheiqistateclockmodel AT patriciovargas ottoenginefortheiqistateclockmodel |