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

We study the thermodynamics and critical behavior of su(m) spin chains of Haldane-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 arbitrary values of m, from which we derive explicit formulas for the energy, entropy, and specific heat per spin. In particular, we find that the specific heat features a single Schottky peak, whose temperature is well approximated for m≲10 by the corresponding temperature for an m-level system with uniformly spaced levels. We show that at low temperatures the free energy per spin of the models under study behaves as that of a one-dimensional conformal field theory with central charge c=m-1 (with the only exception of the Frahm-Inozemtsev chain at zero value of its parameter). However, from a detailed 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.