Exact mean-field solution of a spin chain with short-range and long-range interactions
We consider the transverse field Ising model with additional all-to-all interactions between the spins. We show that a mean-field treatment of this model becomes exact in the thermodynamic limit, despite the presence of 1D short-range interactions. Namely, we show that the eigenstates of the model a...
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| Format: | Article |
| Language: | English |
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SciPost
2023-05-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.14.5.133 |
| _version_ | 1797818886679166976 |
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| author | Etienne Granet |
| author_facet | Etienne Granet |
| author_sort | Etienne Granet |
| collection | DOAJ |
| description | We consider the transverse field Ising model with additional all-to-all interactions between the spins. We show that a mean-field treatment of this model becomes exact in the thermodynamic limit, despite the presence of 1D short-range interactions. Namely, we show that the eigenstates of the model are coherent states with an amplitude that varies through the Hilbert space, within which expectation values of local observables can be computed with mean-field theory. We study then the thermodynamics of the model and identify the different phases. Among its peculiar features, this 1D model possesses a second-order phase transition at finite temperature and exhibits inverse melting. |
| first_indexed | 2024-03-13T09:15:44Z |
| format | Article |
| id | doaj.art-f51e8654b4ec46c3a99cbd3255b8f403 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-13T09:15:44Z |
| publishDate | 2023-05-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-f51e8654b4ec46c3a99cbd3255b8f4032023-05-26T11:32:03ZengSciPostSciPost Physics2542-46532023-05-0114513310.21468/SciPostPhys.14.5.133Exact mean-field solution of a spin chain with short-range and long-range interactionsEtienne GranetWe consider the transverse field Ising model with additional all-to-all interactions between the spins. We show that a mean-field treatment of this model becomes exact in the thermodynamic limit, despite the presence of 1D short-range interactions. Namely, we show that the eigenstates of the model are coherent states with an amplitude that varies through the Hilbert space, within which expectation values of local observables can be computed with mean-field theory. We study then the thermodynamics of the model and identify the different phases. Among its peculiar features, this 1D model possesses a second-order phase transition at finite temperature and exhibits inverse melting.https://scipost.org/SciPostPhys.14.5.133 |
| spellingShingle | Etienne Granet Exact mean-field solution of a spin chain with short-range and long-range interactions SciPost Physics |
| title | Exact mean-field solution of a spin chain with short-range and long-range interactions |
| title_full | Exact mean-field solution of a spin chain with short-range and long-range interactions |
| title_fullStr | Exact mean-field solution of a spin chain with short-range and long-range interactions |
| title_full_unstemmed | Exact mean-field solution of a spin chain with short-range and long-range interactions |
| title_short | Exact mean-field solution of a spin chain with short-range and long-range interactions |
| title_sort | exact mean field solution of a spin chain with short range and long range interactions |
| url | https://scipost.org/SciPostPhys.14.5.133 |
| work_keys_str_mv | AT etiennegranet exactmeanfieldsolutionofaspinchainwithshortrangeandlongrangeinteractions |