AN ESTIMATE OF THE DEPENDENCE OF THE ISING CRITICAL EXPONENTS ON THE LATTICE DIMENSIONALITY

Upper and lower bounds are estimated of the two-point correlation function exponent, eta, of the Ising model, as a function of the lattice dimensionality, d. The average value of these two bounds together with the correlation length critical exponent nu(d) evaluated by Thompson, lead to a set of critical indexes which satisfy the hyperscaling relation. This set of exponents also shows an adequate agreement with the results obtained by Le-Guillou and Zinn-Justin for the Ising model in non-integer dimensions, in a large range of the parameter d.