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Frustrated Ising Model on a Diamond Hierarchical Lattice

A frustrated Ising model on a diamond hierarchical lattice is studied. We obtain the exact partition function of this model and calculate the transition temperature, specific heat, entropy, magnetization, and ferromagnetic correlation function. Depending on the magnitude of a parameter giving the frustration, there exist three types of ground states: ferromagnetic, classical spin-liquid with highly developed short-range order, and paramagnetic. The dependence of the zero-temperature entropy on the frustration parameter has an infinite number of steps. The temperature dependence of the specific heat exhibits many peaks with decreasing temperature and entropy loss. The dominant spin configurations at low temperatures are also specified.