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We study the thermodynamics and critical behavior of su($m$) spin chains ofHaldane-Shastry type at zero chemical potential, both in the $A_{N-1}$ and$BC_N$ cases. We evaluate in closed form the free energy per spin for arbitraryvalues of $m$, from which we derive explicit formulas for the energy, entropyand specific heat per spin. In particular, we find that the specific heatfeatures a single Schottky peak, whose temperature is well approximated for$m\lesssim10$ by the corresponding temperature for an $m$-level system withuniformly spaced levels. We show that at low temperatures the free energy perspin of the models under study behaves as that of a one-dimensional conformalfield theory with central charge $c=m-1$ (with the only exception of theFrahm-Inozemtsev chain with zero value of its parameter). However, from adetailed study of the ground state degeneracy and the low-energy excitations,we conclude that these models are only critical in the antiferromagnetic case,with a few exceptions that we fully specify.

Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type