Calculation of the Free Energy of the Ising Model on a Cayley Tree via the Self-Similarity Method
In this study, an interactive Ising model having the nearest and prolonged next-nearest neighbors defined on a Cayley tree is considered. Inspired by the results obtained for the one-dimensional Ising model, we will construct the partition function and then calculate the free energy of the Ising mod...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/12/703 |
| _version_ | 1797461482089218048 |
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| author | Hasan Akın |
| author_facet | Hasan Akın |
| author_sort | Hasan Akın |
| collection | DOAJ |
| description | In this study, an interactive Ising model having the nearest and prolonged next-nearest neighbors defined on a Cayley tree is considered. Inspired by the results obtained for the one-dimensional Ising model, we will construct the partition function and then calculate the free energy of the Ising model having the prolonged next nearest and nearest neighbor interactions and external field on a two-order Cayley tree using the self-similarity of the semi-infinite Cayley tree. The phase transition problem for the Ising system is investigated under the given conditions. |
| first_indexed | 2024-03-09T17:20:02Z |
| format | Article |
| id | doaj.art-4a5c2488390e425fb0b12aa5d97e6626 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T17:20:02Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-4a5c2488390e425fb0b12aa5d97e66262023-11-24T13:15:42ZengMDPI AGAxioms2075-16802022-12-01111270310.3390/axioms11120703Calculation of the Free Energy of the Ising Model on a Cayley Tree via the Self-Similarity MethodHasan Akın0International Centre for Theoretical Physics (ICTP), Strada Costiera, 11, I-34151 Trieste, ItalyIn this study, an interactive Ising model having the nearest and prolonged next-nearest neighbors defined on a Cayley tree is considered. Inspired by the results obtained for the one-dimensional Ising model, we will construct the partition function and then calculate the free energy of the Ising model having the prolonged next nearest and nearest neighbor interactions and external field on a two-order Cayley tree using the self-similarity of the semi-infinite Cayley tree. The phase transition problem for the Ising system is investigated under the given conditions.https://www.mdpi.com/2075-1680/11/12/703Ising modelpartition functionfree energyphase transition |
| spellingShingle | Hasan Akın Calculation of the Free Energy of the Ising Model on a Cayley Tree via the Self-Similarity Method Axioms Ising model partition function free energy phase transition |
| title | Calculation of the Free Energy of the Ising Model on a Cayley Tree via the Self-Similarity Method |
| title_full | Calculation of the Free Energy of the Ising Model on a Cayley Tree via the Self-Similarity Method |
| title_fullStr | Calculation of the Free Energy of the Ising Model on a Cayley Tree via the Self-Similarity Method |
| title_full_unstemmed | Calculation of the Free Energy of the Ising Model on a Cayley Tree via the Self-Similarity Method |
| title_short | Calculation of the Free Energy of the Ising Model on a Cayley Tree via the Self-Similarity Method |
| title_sort | calculation of the free energy of the ising model on a cayley tree via the self similarity method |
| topic | Ising model partition function free energy phase transition |
| url | https://www.mdpi.com/2075-1680/11/12/703 |
| work_keys_str_mv | AT hasanakın calculationofthefreeenergyoftheisingmodelonacayleytreeviatheselfsimilaritymethod |