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We introduce a class of generalized Lipkin-Meshkov-Glick (gLMG) models withsu$(m)$ interactions of Haldane-Shastry type. We have computed the partitionfunction of these models in closed form by exactly evaluating the partitionfunction of the restriction of a spin chain Hamiltonian of Haldane-Shastry typeto subspaces with well-defined magnon numbers. As a byproduct of our analysis,we have obtained strong numerical evidence of the Gaussian character of thelevel density of the latter restricted Hamiltonians, and studied thedistribution of the spacings of consecutive unfolded levels. We have alsodiscussed the thermodynamic behavior of a large family of su(2) and su(3) gLMGmodels, showing that it is qualitatively similar to that of a two-level system.

Generalized Lipkin-Meshkov-Glick models of Haldane-Shastry type