Amplitude mode in diluted O(N) models

The relativistic O(N) model has recently been shown to exhibit a robust amplitude mode peak in its scalar susceptibility which exhibits scaling in the vicinity of the quantum critical point [PRL 110, 140401 (2013)]. We report on the O(N) model with random site dilution, which we study using the worm algorithm [PRL 87, 160601 (2001)]. We present results for the scalar susceptibility and O(N) conductivity in the critical region and follow the system's behavior as the dilution tends to the percolation threshold.