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

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.

arXiv commentLaTeX, 39 pages, 13 figures

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• The exactly solvable spin Sutherland model of B_N type and its related spin chain
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• Thermodynamics and criticality of supersymmetric spin chains with long-range interactions
• Exact solution and thermodynamics of a spin chain with long-range elliptic interactions
• Thermodynamics of Inozemtsev's Elliptic Spin Chain
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• The open Haldane-Shastry chain: thermodynamics and criticality
• A novel class of translationally invariant spin chains with long-range interactions
• Supersymmetric $t$-$J$ models with long-range interactions: thermodynamics and criticality
• Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type
• Supersymmetric $t$-$J$ models with long-range interactions: partition function and spectrum
• Generalized Lipkin-Meshkov-Glick models of Haldane-Shastry type