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

TL;DR

This paper provides an exact analysis of the thermodynamic properties of Haldane-Shastry spin chains, revealing their equivalence to inhomogeneous classical Ising models and offering new insights into their thermodynamics.

Contribution

It introduces an exact computation of the partition function and free energy for Haldane-Shastry spin chains in a magnetic field, generalizing previous zero-field results.

Findings

Exact partition function for finite spins

Equivalence to inhomogeneous Ising models

Closed-form free energy in the thermodynamic limit

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 thezero 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.