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 $m\lesssim10$ 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 with 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.

我们研究了SU($m$)自旋链的热力学和临界行为 零化学势下的Haldane-Shastry类型，在$A_{N-1}$和 $BC_N$案例。我们以封闭的形式计算任意情况下的每个自旋的自由能 值，由此导出能量、熵的显式公式。 以及每转一圈的比热。特别是，我们发现比热 具有单个肖特基峰，其温度很好地近似于 对于具有$m$级别的系统，相应的温度将减少$m\s 10$ 均匀分布的标高。我们表明，在低温下，每单位自由能 所研究模型的自旋表现为一维共形自旋 中心电荷为$c=m-1$的场论(唯一的例外是 Frahm-Inozemtsev链，其参数为零值)。然而，从一个 详细研究了基态简并和低能激发， 我们得出结论，这些模型只在反铁磁情况下是关键的， 除了我们详细说明的几个例外情况。