Criticality on topologically disordered systems and the Harris criterion

To test the stability of clean critical points against quenched spatial disorder, Harris introduced the criterion dν>2. Its predictions are in agreement with the vast majority of analytical and numerical results on phase transition in disordered systems. However, in systems where disorder arises from random connectivity, a number of violations of the Harris criterion have been reported. We recently introduced [1] a modified stability criterion, (d+1)ν>2, for systems in which the presence of topological constraints suppresses disorder fluctuations, resulting in a violation of the usual Harris criterion. However, some recent results on topologically disordered systems appear to violate even the modified criterion. To uncover the source of such apparent violations we perform a detailed statistical analysis of such systems together with large-scale Monte Carlo simulations.

[1] H. Barghathi and T. Vojta, Phys. Rev. Lett. 113, 120602 (2014).