Frustration in an exactly solvable mixed-spin Ising model with bilinear   and three-site four-spin interactions on a decorated square lattice
  Competitive effects of so-called three-site four-spin interactions, single ion anisotropy and bilinear interactions is studied in the mixed spin-1/2 and spin-1 Ising model on a decorated square lattice. Exploring the decoration-iteration transformation, we have obtained exact closed-form expressions for the partition function and other thermodynamic quantities of the model. From these relations, we have numerically determined ground- state and finite-temperature phase diagrams of the system. We have also investigated temperature variations of the correlation functions, internal energy, entropy, specific heat and Helmholtz free energy of the system. From the physical point of view, the most interesting result represents our observation of a partially ordered ferromagnetic or phase in the system with zero bilinear interactions. It is remarkable, that due to strong frustrations disordered spins survive in the system even at zero temperature, so that the ground state of the system becomes macroscopically degenerate with non-zero entropy. Introduction of arbitrarily small bilinear interaction completely removes degeneracy and the entropy always goes to zero at the the ground state. 
M. Ja\v{s}\v{c}ur, V. \v{S}tub\v{n}a, K. Sza{\l}owski, T. Balcerzak
cond-mat.stat-mech