The Strong-Disorder Renormalization Group (SDRG) introduced by Ma, Dasgupta and Hu and applied by Fisher to the random Ising chain in a transverse field is a powerful tool providing exact results on the low-energy physics of random quantum spin systems. Using SDRG, Senthil and Majumdar showed that the critical behavior of the random q−state quantum Potts and Clock (for strong enough disorder) chain is independent of q. Using an efficient numerical implementation of SDRG due to Kovacs and Igloi, we have estimated the critical exponents ν, d_f , and ψ at the Infinite Disorder Fixed Point of several 2D and 3D random quantum q-state Potts models. Taking into account scaling corrections, critical exponents are found to be q− independent and compatible within error bars with those of the 2D or 3D Ising model. The same analysis for the 2D and 3D random q−state quantum Clock model is under investigation. After quantifying the role of the initial disorder strength, preliminary results indicate an independence of the critical exponents on q too.


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