Thermodynamic ζ functions for Ising models with long-range interactions

The use of cycle expansions for spin systems with long-range interactions is explored numerically. It is found that the thermodynamic {ζ} function is an effective tool, both in practice and in principle, for the study of Ising models with power-law interactions. To deal with phase transitions the cycle expansion is factorized, and accurate phase-transition points for several power-law models are obtained, together with other thermodynamic quantities.