Abstract
We present an exact diagonalization study of the quantum Heisenberg antiferromagnet on the fractal Sierpiński gasket for spin quantum numbers s= 1 2 , 1 and 3 2 . Since the fractal dimension of the Sierpiński gasket is between 1 and 2, we compare the results with the corresponding data of one- and two-dimensional systems. By analyzing the ground-state energy, the low-lying spectrum, the spin–spin correlation and the low-temperature thermodynamics we find arguments that the Heisenberg antiferromagnet on the Sierpiński gasket is probably disordered not only in the extreme quantum case s= 1 2 , but also for s=1 and 3 2 . Moreover, in contrast to the one-dimensional chain, we do not find a distinct behavior between the half-integer and integer-spin Heisenberg models on the Sierpiński gasket. We conclude that magnetic disorder may appear due to the interplay of frustration and strong quantum fluctuations in this spin system with spatial dimension between 1 and 2.
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