Competing multispin interactions

Abstract

A generalized ($D+1$)-dimensional anisotropic Ising model with a combination of multispin interactions in its $D$ dimensions is introduced. A (1 + 1)-dimensional case ($D=1$) with competing two- ($\ensuremath{\sim}{J}_{2}$) and four-spin ($\ensuremath{\sim}{J}_{4}$) couplings was analyzed through its one-dimensional Hamiltonian version with the use of the finite-size scaling method. Whereas for small $\frac{{J}_{4}}{{J}_{2}}$ the transition is of the usual Ising type, for sufficiently large $\frac{{J}_{4}}{{J}_{2}}$ a first-order phase transition occurs. A comparison with other models with competing interactions was made.