On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems characterised by long-range interactions and with critical properties equivalent to those of the class of one-dimensional quantum systems treated by the authors in a previous pub...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/652026 |
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| _version_ | 1850163136789741568 |
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| author | J. Hutchinson J. P. Keating F. Mezzadri |
| author_facet | J. Hutchinson J. P. Keating F. Mezzadri |
| author_sort | J. Hutchinson |
| collection | DOAJ |
| description | We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems characterised by long-range interactions and with critical properties equivalent to those of the class of one-dimensional quantum systems treated by the authors in a previous publication. In particular, we use three approaches: the Trotter-Suzuki mapping, the method of coherent states, and a calculation based on commuting the quantum Hamiltonian with the transfer matrix of a classical system. This enables us to establish universality of certain critical phenomena by extension from the results in the companion paper for the classical systems identified. |
| format | Article |
| id | doaj-art-eb6d06c84de143c2ac677988e51b5b10 |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-eb6d06c84de143c2ac677988e51b5b102025-08-20T02:22:21ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/652026652026On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin SystemsJ. Hutchinson0J. P. Keating1F. Mezzadri2School of Mathematics, University of Bristol, Bristol BS8 1TW, UKSchool of Mathematics, University of Bristol, Bristol BS8 1TW, UKSchool of Mathematics, University of Bristol, Bristol BS8 1TW, UKWe exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems characterised by long-range interactions and with critical properties equivalent to those of the class of one-dimensional quantum systems treated by the authors in a previous publication. In particular, we use three approaches: the Trotter-Suzuki mapping, the method of coherent states, and a calculation based on commuting the quantum Hamiltonian with the transfer matrix of a classical system. This enables us to establish universality of certain critical phenomena by extension from the results in the companion paper for the classical systems identified.http://dx.doi.org/10.1155/2015/652026 |
| spellingShingle | J. Hutchinson J. P. Keating F. Mezzadri On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems Advances in Mathematical Physics |
| title | On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems |
| title_full | On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems |
| title_fullStr | On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems |
| title_full_unstemmed | On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems |
| title_short | On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems |
| title_sort | on relations between one dimensional quantum and two dimensional classical spin systems |
| url | http://dx.doi.org/10.1155/2015/652026 |
| work_keys_str_mv | AT jhutchinson onrelationsbetweenonedimensionalquantumandtwodimensionalclassicalspinsystems AT jpkeating onrelationsbetweenonedimensionalquantumandtwodimensionalclassicalspinsystems AT fmezzadri onrelationsbetweenonedimensionalquantumandtwodimensionalclassicalspinsystems |