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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 652026, 18 pages
Research Article

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

School of Mathematics, University of Bristol, Bristol BS8 1TW, UK

Received 31 August 2015; Accepted 1 November 2015

Academic Editor: Pierluigi Contucci

Copyright © 2015 J. Hutchinson et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.