A new approach to description of phase transitions in spin systems

Spin systems with a long-range sign-alternating interaction undergoing a fluctuation phase transition are investigated. A new approach to the calculation of corresponding thermodynamic quantities is suggested. It is based on the summation of the principal part of high-temperature series in z-1 performed in a way which leads to a correct description of the critical behavior in the one-loop approxiamtion (z is the number of the neighbor spins interacting with a given one). The accuracy of the method is of a universal nature; for three-dimensional spin systems the error of some particular calculations is below 2%.