On relations between one-dimensional quantum and two-dimensional classical spin systems

J. Hutchinson; J. P. Keating; F. Mezzadri

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arXiv · 1503.07712

On relations between one-dimensional quantum and two-dimensional classical spin systems

J. Hutchinson·J. P. Keating·F. Mezzadri

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Abstract

We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion paper (J. Hutchinson, J. P. Keating, and F. Mezzadri, arXiv:1503.05732). 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 our previous article for the classical systems identified.

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BibTeX RIS

J. Hutchinson, J. P. Keating, F. Mezzadri. 2015-03-26. On relations between one-dimensional quantum and two-dimensional classical spin systems. https://arxiv.org/abs/1503.07712

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