Critical behavior of the ferromagnetic ising chain with interaction $J_{ij}=|i-j|^{-2}$

For the one-dimensional ferromagnetic Isiag model with interaction that decreases inversely as the square of the distance between the lattice sites, high-temperature expansions of the susceptibility and specific heat are calculated to the eighth and ninth orders, respectively, in the reciprocal temperature. Analysis of the expansion of the susceptibility indicates that at the critical point its logarithm diverges in accordance with a power law with exponent $\nu=0,55\pm 0,03$. This estimate is close to the value $\nu=0.5$ obtained earlier by the renormalization-group method and is the first numerical confirmation of the predictions of the renormalization-group approach for systems with long-range interaction.