Solution and Critical Behavior of Some "Three-Dimensional" Ising Models with a Four-Spin Interaction

An exact solution is obtained for some "three-dimensional" Ising models with a four-spin interaction. The spontaneous magnetization is vanishing for all temperatures. The temperature derivative of the susceptibility shows a divergence of the form ${(T_c-T)}^{\frac{-7\mathrm{}}{8}}$ below the critical point. The specific heat shows a logarithmic singularity. Several other related models are introduced with new types of singularities.