Yang–Lee and Fisher zeros of multisite interaction Ising models on the Cayley-type lattices

Abstract 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.