Mandelbrot-like and Julia Sets Associated with Yang-Lee and Fisher Zeros of Ising Models

Article type: Research Article

Authors: Ananikian, Nerses | Ghulghazaryan, Ruben^{; 1}

Affiliations: Yerevan Physics Institute, Alikhanian Brothers 2, 375036 Yerevan, Armenia

Correspondence: [1] The address for manuscript correspondence: Ruben Ghulghazaryan, Yerevan Physics Institute, Alikhanian Brothers 2, 375036 Yerevan, Armenia. Phone (office): 374-1-350150. Fax: 374-1-350030. E-mail: [email protected].

Abstract: A method for numerical investigation of the Yang-Lee and Fisher zeros of models defined on Cayley-type lattices is given. The method is based on testing the convergence of critical orbits of the corresponding 1D rational mapping to any attracting periodic point. The Yang-Lee and Fisher zeros of multisite interaction Ising model are investigated on Cayley-type lattices. A corresponding C++ program is given in the appendix. Our numerical experiments show that copies of the Mandelbrot set of the quadratic mapping z → z2 + c arise in the pictures of Yang-Lee and Fisher zeros. This phenomenon is known as the universality of the Mandelbrot set.

Keywords: Cayley-type lattice, Mandelbrot set, Julia set, Fisher zeros, Yang-Lee zeros

DOI: 10.3233/JCM-2002-21-211

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 2, no. 1-2, pp. 75-86, 2002