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.