We investigate in the limit as the range of part of the interspin interaction becomes indefinitely great, but is still small compared to the size of the system, the behavior of Ising models which have, in addition, a residual short-range interaction. We find that the only possible type of transition in this limit is the familiar Bragg-Williams type. We also investigate the passage of the three-dimensional Ising model on the simple cubic lattice to the long-range limit from the short-range limit, dimension by dimension.

• Received 9 January 1963

DOI:https://doi.org/10.1103/PhysRev.130.1406