Spin models subject to both nearest-neighbor and equivalent-neighbor interactions are studied. The free energy of these models is related to the free energy of the nearest-neighbor spin models in a magnetic field. The scaling exponent for equivalent-neighbor interactions is calculated, and crossover from Ising to mean-field criticality is described in arbitrary dimensions. Interesting multicritical behavior is observed for antiferromagnetic nearest-neighbor interactions.

• Received 24 February 1983

DOI:https://doi.org/10.1103/PhysRevB.28.244