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Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models

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Enciso, Alberto and Finkel Morgenstern, Federico and González López, Artemio (2012) Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models. Annals of physics, 327 (11). pp. 2627-2665. ISSN 0003-4916

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Official URL: http://dx.doi.org/ 10.1016/j.aop.2012.07.010


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Abstract

We study the thermodynamic properties of spin chains of Haldane-Shastry type associated with the A(N-1) root system in the presence of a uniform external magnetic field. To this end, we exactly compute the partition function of these models for an arbitrary finite number of spins. We then show that these chains are equivalent to a suitable inhomogeneous classical Ising model in a spatially dependent magnetic field, generalizing the results of Basu-Mallick et al. for the zero magnetic field case. Using the standard transfer matrix approach, we are able to compute in closed form the free energy per site in the thermodynamic limit. We perform a detailed analysis of the chains' thermodynamics in a unified way, with special emphasis on the zero field and zero temperature limits. Finally, we provide a novel interpretation of the thermodynamic quantities of spin chains of Haldane-Shastry type as weighted averages of the analogous quantities over an ensemble of classical Ising models.


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Additional Information:

©2012 Elsevier Inc. All rights reserved.
This work was supported in part by the MICINN and the UCM–Banco Santander under grants no. FIS2011-22566 and GR35/10-A-910556.

Uncontrolled Keywords:Spin chains of haldane–shastry type; Vertex models; Transfer matrix method; Thermodynamic limit
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:31239
Deposited On:02 Jul 2015 15:20
Last Modified:10 Dec 2018 15:09

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