Phase transitions in systems with multispin interactions

An Ising-type model including $n$-spin nearest-neighbor interactions is introduced. The ground-state properties of its Hamiltonian version are studied in one and two dimensions. The model is self-dual in one dimension. The mean-field theory indicates that for $n>\mathrm{}{n}_c$ the transition may become first order. Finite-size scaling suggests that $n_c=4\mathrm{}$ in one dimension. The critical exponents as functions of $n$ are estimated.