  We investigate a frustrated Heisenberg spin-1/2 antiferromagnet on a fractal
lattice of dimension d=ln3/ln2 (Sierpinski gasket). Calculations were performed
using (a) exact diagonalization of all eigenstates and eigenvectors for systems
up to N=15 and (b) the Decoupled-Cell Quantum-Monte-Carlo method for systems up
to N=366. We present the low-lying spectrum and the specific heat. The specific
heat shows a second maximum in the low-temperature region. This behavior is
similar to the behavior of the quantum Heisenberg antiferromagnet on a kagome
lattice and suggests a disordered ground state and a spin gap in the considered
system.
