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We study the thermodynamic properties of spin chains of Haldane-Shastry typeassociated with the A_{N-1} root system in the presence of a uniform externalmagnetic field. To this end, we exactly compute the partition function of thesemodels for an arbitrary finite number of spins. We then show that these chainsare equivalent to a suitable inhomogeneous classical Ising model in a spatiallydependent magnetic field, generalizing the results of Basu-Mallick et al. forthezero magnetic field case. Using the standard transfer matrix approach, weare able to compute in closed form the free energy per site in thethermodynamic limit. We perform a detailed analysis of the chains'thermodynamics in a unified way, with special emphasis on the zero field andzero temperature limits. Finally, we provide a novel interpretation of thethermodynamic quantities of spin chains of Haldane-Shastry type as weightedaverages of the analogous quantities over an ensemble of classical Isingmodels.

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