Yang-Lee and Fisher Zeros of Multisite Interaction Ising Models on the Cayley-type Lattices

A general analytical formula for recurrence relations of multisite interaction Ising models in an external magnetic field on the Cayley-type lattices is derived. Using the theory of complex analytical dynamics on the Riemann sphere, a numerical algorithm to obtain Yang-Lee and Fisher zeros of the models is developed. It is shown that the sets of Yang-Lee and Fisher zeros are almost always fractals, that could be associated with Mandelbrot-like sets on the complex magnetic field and temperature planes respectively.Comment: 9 pages, 3 figures; with minor correction

Magnetizaition plateau of the compound K₃Cu₃AlO₂(SO₄)₄

Using the density matrix renormalization group method of the spin 1/2 magnetic behavior of the compound K3Cu3AlO2(SO4)4, which represents the physical realization of the diamond chain, was studied. For the values J1 = J3 = 132K, J2 = 336K of coupling constants we obtained the magnetization plateau in the region 50-300 T of the external magnetic field. We used the ALPS (Algorithms and Libraries for Physics Simulations) library for the numerical calculations