Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpi´nski gasket
Meng Wang¹, Shi-Ju Ran¹, Tao Liu¹, Yang Zhao², Qing-Rong Zheng¹, and Gang Su^1,a
1 Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, School of Physics, University
of Chinese Academy of Sciences, P.O. Box 4588, Beijing 100049, P.R. China
² Department of Physics and Astronomy, University of Manitoba, Winnipeg, R3T 2N2, Canada
Received 15 September 2015 / Received in final form 15 December 2015
Published online 1 February 2016 – c EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2016

The anisotropic antiferromagnetic Ising model on the fractal Sierpi´nski gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with 0 ≤ Jb/Ja < 1, and an interesting crossover behavior between different phases at Jb/Ja = 1 is unveiled, whose dynamics can be described by the Jb/Ja-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpi´nski gasket are obtained in both the 1/3 plateau disordered phase and the 5/9 plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpi´nski gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.