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: J. Hutchinson, J. P. Keating, F. Mezzadri
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2015/652026
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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.
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issn 1687-9120
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language English
publishDate 2015-01-01
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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
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AT jpkeating onrelationsbetweenonedimensionalquantumandtwodimensionalclassicalspinsystems
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