Diagrammatic damage spreading in the quantum Heisenberg ferromagnet

The Handscomb Monte Carlo method is a powerful tool for the investigation of the critical properties of quantum spin models. The sample space in this technique is constructed over the space of ordered Mayerʹs diagrams and it is the diagrammatic series of the partition function that is calculated by means of the Monte Carlo method. In this work, we apply a damage-spreading algorithm to study the quantum Heisenberg 3D ferromagnet. The damage is introduced as a perturbation in the bond structure of the Mayerʹs diagrams. A cyclic Hamming distance is shown to be closely related to the static spin susceptibility. Using a phenomenological renormalization group analysis we show that the cyclic Hamming distance scales near Tc as NDc=Lγ/νg(tL1/ν), with ν=0.7 and γ/ν=1.99.