Eur. Phys. J. B (2016) 89: 27
https://doi.org/10.1140/epjb/e2015-60745-5

Regular Article

Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket

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

^a e-mail: gsu@ucas.ac.cn

Received: 15 September 2015
Received in final form: 15 December 2015
Published online: 1 February 2016

Abstract

The anisotropic antiferromagnetic Ising model on the fractal Sierpiński 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 ≤ J_b/J_a< 1, and an interesting crossover behavior between different phases at J_b/J_a = 1 is unveiled, whose dynamics can be described by the J_b/J_a-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 Sierpiński 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 Sierpiński gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.