On Relations between One‐Dimensional Quantum and Two‐Dimensional Classical Spin Systems

J. Hutchinson, J. P. Keating and F. Mezzadri

Advances in Mathematical Physics, 2015, vol. 2015, issue 1

Abstract: 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.

Date: 2015
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https://doi.org/10.1155/2015/652026

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:652026

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