We present a construction of a new integrable model as an infinite limit of Calogero models of N particles with spin. It is implemented in the multicomponent Fock space. Explicit formulas for Dunkl operators, the Yangian generators in the multicomponent Fock space are presented. The classical limit of the system is examined.

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We describe integrable elliptic q-deformed anisotropic long-range spin chain. The derivation is based on our recent construction for commuting anisotropic elliptic spin Ruijsenaars–Macdonald operators. We prove that the Polychronakos freezing trick can be applied to these operators, thus providing the commuting set of Hamiltonians for long-range spin chain constructed by means of the elliptic Baxter-Belavin G L M R -matrix. Namely, we show that the freezing trick is reduced to a set of elliptic function identities, which are then proved. These identities can be treated as conditions for equilibrium position in the underlying classical spinless Ruijsenaars–Schneider model. Trigonometric degenerations are studied as well. For example, in M = 2 case our construction provides q-deformation for anisotropic XXZ Haldane–Shastry model. The standard Haldane–Shastry model and its Uglov’s q-deformation based on U q ( g l ˆ M ) XXZ R-matrix are included into consideration by separate verification.

We present a construction of an integrable model as a projective type limit of Calogero-Sutherland models of N fermionic particles, when N tends to infinity. Explicit formulas for limits of Dunkl operators and of commuting Hamiltonians by means of vertex operators are given.

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