The exactly solvable spin Sutherland model of image type and its related spin chain Original Research Article

We compute the spectrum of the image spin Sutherland model of image type, including the exact degeneracy of all energy levels. By studying the large coupling constant limit of this model and of its scalar counterpart, we evaluate the partition function of their associated spin chain of Haldane–Shastry type in closed form. With the help of the formula for the partition function thus obtained we study the chainʼs spectrum, showing that it cannot be obtained as a limiting case of its image counterpart. The structure of the partition function also suggests that the spectrum of the Haldane–Shastry spin chain of image type is equivalent to that of a suitable vertex model, as is the case for its image counterpart, and that the density of its eigenvalues is normally distributed when the number of sites N tends to infinity. We analyze this last conjecture numerically using again the explicit formula for the partition function, and check its validity for several values of N and m.